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Finding integrals by integration by partial fractions

Find the integral $\int_{ }^{ }\frac{\left(x^2+1\ \right)}{\left(x^{^2}-5x+6\right)}dx$ using partial fraction method

$x-5\log\left|x-2\right|-\log\left|x+2\right|+c$

$x-5\log\left|x-2\right|+c$

$10\log\left|x-3\right|+c$

Find the integral $\int_{ }^{ }\frac{6}{\left(x^{^2}-1\right)}dx$ using partial fraction method.

$-3\log\left|x+1\right|+3\log\left|x-1\right|+c$

$-3\log\left|x-2\right|+3\left|x-3\right|+c$

Find the integral $\int_{ }^{ }\frac{1}{\left(x^{^2}-9\right)}dx$ using partial fraction method

$4\log\left|x+2\right|-\log\left|x+1\right|+c$

$\frac{1}{6}\left[\log\left|x-3\right|-\log\left|x+3\right|\right]+c$

Find the integral $\int_{ }^{ }\frac{\left(3x+2\right)}{\left(x+1\right)\left(x+2\right)}dx$ using partial fraction method

$4\log\left|x+2\right|-\log\left|x+1\right|+c$

$4\log\left|x-1\right|+5\log\left|x+3\right|+c$

Find the integral $\int_{ }^{ }\frac{\left(x+1\right)}{\left(x-2\right)}dx$ using partial fraction method

$\left(x+3\right)\ln\left|x+1\right|+c$

$\left(x-3\right)\ln\left|x+1\right|+c$

$x+\ln\left|x-2\right|+c$

Find the integral $\int_{ }^{ }\frac{\left(2x+3\right)}{\left(x^{2\ }-9\right)}dx$ using partial fraction method

$\ln\left|x^2\right|-2x+2\ln\left|x+1\right|+c$

$\frac{1}{2}\ln\left(x-3\right)^3\left(x+3\right)+c$

$x^2-2x+2\ln\left|x+1\right|+c$

Find the integral $\int_{ }^{ }\frac{1}{\left(x+1\right)\left(x+2\right)}dx$ using partial fraction method

$4\log\left|x+2\right|-\log\left|x+1\right|$ +c

$\log\left|x+1\right|-\log\left|x+2\right|+c$

Find the integral $\int_{ }^{ }\frac{2x^2}{x+1}dx$ using partial fraction method

$x^2-2x\ln\left|4x\right|+c$

$4\ln\left|x\right|+c$

$x^2-2x+2\ln\left|x+1\right|+c$

Find the integral $\int_{ }^{ }\frac{\left(x-7\right)}{\left(x^{^2}+2x-3\right)}dx$ using partial fraction method

$-3\log\left|x+1\right|+3\log\left|x-1\right|+c$

$\frac{1}{2}\left[-3\log\right|x-1\left|+5\log\right|x+3\left|\right]+c$

Find the integral $\int_{ }^{ }\frac{\left(6x+13\right)}{\left(x^{2\ }+5x+6\right)}dx$ using partial fraction method

$\ln\left[\right|x+2\left|\right|x+3\left|^3\right]+c$

$\ln\left[\right|x+2\left|\right|x+3\left|^5\right]+c$

Questions

Time

Score

Finding integrals by integration by partial fractions

Find the integral $\int_{ }^{ }\frac{\left(x^2+1\ \right)}{\left(x^{^2}-5x+6\right)}dx$ using partial fraction method

$x-5\log\left|x-2\right|-\log\left|x+2\right|+c$

$x-5\log\left|x-2\right|+c$

$10\log\left|x-3\right|+c$

Find the integral $\int_{ }^{ }\frac{6}{\left(x^{^2}-1\right)}dx$ using partial fraction method.

$-3\log\left|x+1\right|+3\log\left|x-1\right|+c$

$-3\log\left|x-2\right|+3\left|x-3\right|+c$

Find the integral $\int_{ }^{ }\frac{1}{\left(x^{^2}-9\right)}dx$ using partial fraction method

$4\log\left|x+2\right|-\log\left|x+1\right|+c$

$\frac{1}{6}\left[\log\left|x-3\right|-\log\left|x+3\right|\right]+c$

Find the integral $\int_{ }^{ }\frac{\left(3x+2\right)}{\left(x+1\right)\left(x+2\right)}dx$ using partial fraction method

$4\log\left|x+2\right|-\log\left|x+1\right|+c$

$4\log\left|x-1\right|+5\log\left|x+3\right|+c$

Find the integral $\int_{ }^{ }\frac{\left(x+1\right)}{\left(x-2\right)}dx$ using partial fraction method

$\left(x+3\right)\ln\left|x+1\right|+c$

$\left(x-3\right)\ln\left|x+1\right|+c$

$x+\ln\left|x-2\right|+c$

Find the integral $\int_{ }^{ }\frac{\left(2x+3\right)}{\left(x^{2\ }-9\right)}dx$ using partial fraction method

$\ln\left|x^2\right|-2x+2\ln\left|x+1\right|+c$

$\frac{1}{2}\ln\left(x-3\right)^3\left(x+3\right)+c$

$x^2-2x+2\ln\left|x+1\right|+c$

Find the integral $\int_{ }^{ }\frac{1}{\left(x+1\right)\left(x+2\right)}dx$ using partial fraction method

$4\log\left|x+2\right|-\log\left|x+1\right|$ +c

$\log\left|x+1\right|-\log\left|x+2\right|+c$

Find the integral $\int_{ }^{ }\frac{2x^2}{x+1}dx$ using partial fraction method

$x^2-2x\ln\left|4x\right|+c$

$4\ln\left|x\right|+c$

$x^2-2x+2\ln\left|x+1\right|+c$

Find the integral $\int_{ }^{ }\frac{\left(x-7\right)}{\left(x^{^2}+2x-3\right)}dx$ using partial fraction method

$-3\log\left|x+1\right|+3\log\left|x-1\right|+c$

$\frac{1}{2}\left[-3\log\right|x-1\left|+5\log\right|x+3\left|\right]+c$

Find the integral $\int_{ }^{ }\frac{\left(6x+13\right)}{\left(x^{2\ }+5x+6\right)}dx$ using partial fraction method

$\ln\left[\right|x+2\left|\right|x+3\left|^3\right]+c$

$\ln\left[\right|x+2\left|\right|x+3\left|^5\right]+c$

Incorrect

Great!

Questions

Time

Score

Finding integrals by integration by partial fractions

Find the integral ﻿∫(x2+1 )(x2−5x+6)dx\int_{ }^{ }\frac{\left(x^2+1\ \right)}{\left(x^{^2}-5x+6\right)}dx∫​(x2−5x+6)(x2+1 )​dx﻿ using partial fraction method

﻿x−5log⁡∣x−2∣−log⁡∣x+2∣+cx-5\log\left|x-2\right|-\log\left|x+2\right|+cx−5log∣x−2∣−log∣x+2∣+c﻿

﻿x−5log⁡∣x−2∣+cx-5\log\left|x-2\right|+cx−5log∣x−2∣+c﻿

﻿10log⁡∣x−3∣+c10\log\left|x-3\right|+c10log∣x−3∣+c﻿

Find the integral ﻿∫6(x2−1)dx\int_{ }^{ }\frac{6}{\left(x^{^2}-1\right)}dx∫​(x2−1)6​dx﻿ using partial fraction method.

﻿−3log⁡∣x+1∣+3log⁡∣x−1∣+c-3\log\left|x+1\right|+3\log\left|x-1\right|+c−3log∣x+1∣+3log∣x−1∣+c﻿

﻿−3log⁡∣x−2∣+3∣x−3∣+c-3\log\left|x-2\right|+3\left|x-3\right|+c−3log∣x−2∣+3∣x−3∣+c﻿

Find the integral﻿∫1(x2−9)dx\int_{ }^{ }\frac{1}{\left(x^{^2}-9\right)}dx∫​(x2−9)1​dx﻿ using partial fraction method

﻿4log⁡∣x+2∣−log⁡∣x+1∣+c4\log\left|x+2\right|-\log\left|x+1\right|+c4log∣x+2∣−log∣x+1∣+c﻿

﻿16[log⁡∣x−3∣−log⁡∣x+3∣]+c\frac{1}{6}\left[\log\left|x-3\right|-\log\left|x+3\right|\right]+c61​[log∣x−3∣−log∣x+3∣]+c﻿

Find the integral ﻿∫(3x+2)(x+1)(x+2)dx\int_{ }^{ }\frac{\left(3x+2\right)}{\left(x+1\right)\left(x+2\right)}dx∫​(x+1)(x+2)(3x+2)​dx﻿ using partial fraction method

﻿4log⁡∣x+2∣−log⁡∣x+1∣+c4\log\left|x+2\right|-\log\left|x+1\right|+c4log∣x+2∣−log∣x+1∣+c﻿

﻿4log⁡∣x−1∣+5log⁡∣x+3∣+c4\log\left|x-1\right|+5\log\left|x+3\right|+c4log∣x−1∣+5log∣x+3∣+c﻿

Find the integral ﻿∫(x+1)(x−2)dx\int_{ }^{ }\frac{\left(x+1\right)}{\left(x-2\right)}dx∫​(x−2)(x+1)​dx﻿ using partial fraction method

﻿(x+3)ln⁡∣x+1∣+c\left(x+3\right)\ln\left|x+1\right|+c(x+3)ln∣x+1∣+c﻿

﻿(x−3)ln⁡∣x+1∣+c\left(x-3\right)\ln\left|x+1\right|+c(x−3)ln∣x+1∣+c﻿

﻿x+ln⁡∣x−2∣+cx+\ln\left|x-2\right|+cx+ln∣x−2∣+c﻿

Find the integral﻿∫(2x+3)(x2 −9)dx\int_{ }^{ }\frac{\left(2x+3\right)}{\left(x^{2\ }-9\right)}dx∫​(x2 −9)(2x+3)​dx﻿ using partial fraction method

﻿ln⁡∣x2∣−2x+2ln⁡∣x+1∣+c\ln\left|x^2\right|-2x+2\ln\left|x+1\right|+cln∣∣​x2∣∣​−2x+2ln∣x+1∣+c﻿

﻿12ln⁡(x−3)3(x+3)+c\frac{1}{2}\ln\left(x-3\right)^3\left(x+3\right)+c21​ln(x−3)3(x+3)+c﻿

﻿x2−2x+2ln⁡∣x+1∣+cx^2-2x+2\ln\left|x+1\right|+cx2−2x+2ln∣x+1∣+c﻿

Find the integral ﻿∫1(x+1)(x+2)dx\int_{ }^{ }\frac{1}{\left(x+1\right)\left(x+2\right)}dx∫​(x+1)(x+2)1​dx﻿ using partial fraction method

﻿4log⁡∣x+2∣−log⁡∣x+1∣4\log\left|x+2\right|-\log\left|x+1\right|4log∣x+2∣−log∣x+1∣﻿ +c

﻿log⁡∣x+1∣−log⁡∣x+2∣+c\log\left|x+1\right|-\log\left|x+2\right|+clog∣x+1∣−log∣x+2∣+c﻿

Find the integral ﻿∫2x2x+1dx\int_{ }^{ }\frac{2x^2}{x+1}dx∫​x+12x2​dx﻿ using partial fraction method

﻿x2−2xln⁡∣4x∣+cx^2-2x\ln\left|4x\right|+cx2−2xln∣4x∣+c﻿

﻿4ln⁡∣x∣+c4\ln\left|x\right|+c4ln∣x∣+c﻿

﻿x2−2x+2ln⁡∣x+1∣+cx^2-2x+2\ln\left|x+1\right|+cx2−2x+2ln∣x+1∣+c﻿

Find the integral ﻿∫(x−7)(x2+2x−3)dx\int_{ }^{ }\frac{\left(x-7\right)}{\left(x^{^2}+2x-3\right)}dx∫​(x2+2x−3)(x−7)​dx﻿ using partial fraction method

﻿−3log⁡∣x+1∣+3log⁡∣x−1∣+c-3\log\left|x+1\right|+3\log\left|x-1\right|+c−3log∣x+1∣+3log∣x−1∣+c﻿

﻿12[−3log⁡∣x−1∣+5log⁡∣x+3∣]+c\frac{1}{2}\left[-3\log\right|x-1\left|+5\log\right|x+3\left|\right]+c21​[−3log∣x−1∣+5log∣x+3∣]+c﻿

Find the integral ﻿∫(6x+13)(x2 +5x+6)dx\int_{ }^{ }\frac{\left(6x+13\right)}{\left(x^{2\ }+5x+6\right)}dx∫​(x2 +5x+6)(6x+13)​dx﻿ using partial fraction method

﻿ln⁡[∣x+2∣∣x+3∣3]+c\ln\left[\right|x+2\left|\right|x+3\left|^3\right]+cln[∣x+2∣∣x+3∣∣​3]+c﻿

﻿ln⁡[∣x+2∣∣x+3∣5]+c\ln\left[\right|x+2\left|\right|x+3\left|^5\right]+cln[∣x+2∣∣x+3∣∣​5]+c﻿

Incorrect

Great!

Find the integral $\int_{ }^{ }\frac{\left(x^2+1\ \right)}{\left(x^{^2}-5x+6\right)}dx$ using partial fraction method

$x-5\log\left|x-2\right|-\log\left|x+2\right|+c$

$x-5\log\left|x-2\right|+c$

$10\log\left|x-3\right|+c$

Find the integral $\int_{ }^{ }\frac{6}{\left(x^{^2}-1\right)}dx$ using partial fraction method.

$-3\log\left|x+1\right|+3\log\left|x-1\right|+c$

$-3\log\left|x-2\right|+3\left|x-3\right|+c$

Find the integral $\int_{ }^{ }\frac{1}{\left(x^{^2}-9\right)}dx$ using partial fraction method

$4\log\left|x+2\right|-\log\left|x+1\right|+c$

$\frac{1}{6}\left[\log\left|x-3\right|-\log\left|x+3\right|\right]+c$

Find the integral $\int_{ }^{ }\frac{\left(3x+2\right)}{\left(x+1\right)\left(x+2\right)}dx$ using partial fraction method

$4\log\left|x+2\right|-\log\left|x+1\right|+c$

$4\log\left|x-1\right|+5\log\left|x+3\right|+c$

Find the integral $\int_{ }^{ }\frac{\left(x+1\right)}{\left(x-2\right)}dx$ using partial fraction method

$\left(x+3\right)\ln\left|x+1\right|+c$

$\left(x-3\right)\ln\left|x+1\right|+c$

$x+\ln\left|x-2\right|+c$

Find the integral $\int_{ }^{ }\frac{\left(2x+3\right)}{\left(x^{2\ }-9\right)}dx$ using partial fraction method

$\ln\left|x^2\right|-2x+2\ln\left|x+1\right|+c$

$\frac{1}{2}\ln\left(x-3\right)^3\left(x+3\right)+c$

$x^2-2x+2\ln\left|x+1\right|+c$

Find the integral $\int_{ }^{ }\frac{1}{\left(x+1\right)\left(x+2\right)}dx$ using partial fraction method

$4\log\left|x+2\right|-\log\left|x+1\right|$ +c

$\log\left|x+1\right|-\log\left|x+2\right|+c$

Find the integral $\int_{ }^{ }\frac{2x^2}{x+1}dx$ using partial fraction method

$x^2-2x\ln\left|4x\right|+c$

$4\ln\left|x\right|+c$

$x^2-2x+2\ln\left|x+1\right|+c$

Find the integral $\int_{ }^{ }\frac{\left(x-7\right)}{\left(x^{^2}+2x-3\right)}dx$ using partial fraction method

$-3\log\left|x+1\right|+3\log\left|x-1\right|+c$

$\frac{1}{2}\left[-3\log\right|x-1\left|+5\log\right|x+3\left|\right]+c$

Find the integral $\int_{ }^{ }\frac{\left(6x+13\right)}{\left(x^{2\ }+5x+6\right)}dx$ using partial fraction method

$\ln\left[\right|x+2\left|\right|x+3\left|^3\right]+c$

$\ln\left[\right|x+2\left|\right|x+3\left|^5\right]+c$