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∫(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
باستخدام طريقة الكسر الجزئي
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
∫2x2x+1dx\int_{ }^{ }\frac{2x^2}{x+1}dx∫x+12x2dx
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
∫(2x+3)(x2−9)dx\int_{ }^{ }\frac{\left(2x+3\right)}{\left(x^2-9\right)}dx∫(x2−9)(2x+3)dx
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)+c21ln(x−3)3(x+3)+c
∫(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
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
∫6(x2−1)dx\int_{ }^{ }\frac{6}{\left(x^{^2}-1\right)}dx∫(x2−1)6dx
−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
∫1(x+1)(x+2)dx\int_{ }^{ }\frac{1}{\left(x+1\right)\left(x+2\right)}dx∫(x+1)(x+2)1dx
log∣x+1∣−log∣x+2∣+c\log\left|x+1\right|-\log\left|x+2\right|+clog∣x+1∣−log∣x+2∣+c
∫(x+1)(x−2)dx\int_{ }^{ }\frac{\left(x+1\right)}{\left(x-2\right)}dx∫(x−2)(x+1)dx
(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
∫(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
ln[∣x+2∣∣x+3∣3]+c\ln\left[\left|x+2\right|\left|x+3\right|^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
∫(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
12[−3log∣x−1∣+5log∣x+3∣+c]\frac{1}{2}\left[-3\log\left|x-1\right|+5\log\left|x+3\right|+c\right]21[−3log∣x−1∣+5log∣x+3∣+c]
∫1(x2 −9)dx\int_{ }^{ }\frac{1}{\left(x^{2\ }-9\right)}dx∫(x2 −9)1dx
16[[log∣x−3∣−log∣x+3∣]+c]\frac{1}{6}\left[\left[\log\left|x-3\right|-\log\left|x+3\right|\right]+c\right]61[[log∣x−3∣−log∣x+3∣]+c]
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