|BSM

Questions

1 / 10

Time

Score

Finding integrals by substitution method

Determine the integral $\int_{ }^{ }\left(ax+b\right)^ndx$ using substitution method

$\frac{\left(ax+b\right)^{n+1}}{an}+c$

$\frac{\left(ax+b\right)^n}{a\left(n+1\right)}+c$

$\frac{\left(ax+b\right)^{n+1}}{a\left(n+1\right)}+c$

Determine the integral $\int_{ }^{ }\left(x^2+1\right)^2dx$ using substitution method

$\frac{x^5}{5}+\frac{2x^3}{3}+c$

$\frac{2x^3}{3}+x+c$

$\frac{x^5}{5}+\frac{2x^3}{3}+x+c$

Determine the integral $\int_{ }^{ }\left[\frac{\sin x}{x}\right]dx$ using substitution method

$\frac{\sec^2x}{2}+c$

$\frac{\sec^3x}{2}+c$

$\frac{\sec^4x}{2}+c$

Determine the integral $\int_{ }^{ }\left[\frac{\sin x}{x}\right]dx$ using substitution method

$\frac{\sin^4x}{4}+c$

$\frac{\sec^3x}{2}+c$

$\frac{\sec^4x}{2}+c$

Determine the integral $\int_{ }^{ }\left[x\cos x\right]dx$ using substitution method

$-\frac{\cos x^2}{4}+c$

$\frac{\sin x^4}{4}+c$

$\frac{\sin^4x^{ }}{4}+c$

Determine the integral $\int_{ }^{ }x\left(x^2+1\right)^{100}dx$ using substitution method

$\frac{\left(x^2+1\right)^{109}}{109}+c$

$-\frac{\left(x^2+1\right)^{101}}{202}+c$

$-\frac{\left(x^2+1\right)^{101}}{119}+c$

Determine the integral $\int_{ }^{ }\sin\left(2x+1\right)dx$ using substitution method

$\frac{\left(2x+1\right)}{2}+c$

$\frac{\cos\left(2x+1\right)}{2}+c$

$\frac{-\cos\left(2x+1\right)}{2}+c$

Determine the integral $\int_{ }^{ }2x\left[\sin\sin x^2\right]dx$ using substitution method

$-\cos x^2+c$

$\sin x^2+c$

$\sin x+c$

Determine the integral $\int_{ }^{ }\left(1-x\right)^9dx$ using substitution method

$-\frac{\left(1-x\right)^9}{10}-\cos x^2+c$

$-\frac{\left(1-x\right)^{10}}{10}+c$

$-\frac{\left(1-x\right)^{10}}{9}+c$

Determine the integral $\int_{ }^{ }\left(2x+1\right)^3dx$ using substitution method

$\frac{\left(2x+1\right)^3}{8}+c$

$\frac{\left(2x+1\right)^4}{4}+c$

$\frac{\left(2x+1\right)^4}{8}+c$

Questions

Time

Score

Finding integrals by substitution method

Determine the integral﻿∫(ax+b)ndx\int_{ }^{ }\left(ax+b\right)^ndx∫​(ax+b)ndx﻿ using substitution method

﻿(ax+b)n+1an+c\frac{\left(ax+b\right)^{n+1}}{an}+can(ax+b)n+1​+c﻿

﻿(ax+b)na(n+1)+c\frac{\left(ax+b\right)^n}{a\left(n+1\right)}+ca(n+1)(ax+b)n​+c﻿

﻿(ax+b)n+1a(n+1)+c\frac{\left(ax+b\right)^{n+1}}{a\left(n+1\right)}+ca(n+1)(ax+b)n+1​+c﻿

Determine the integral﻿∫(x2+1)2dx\int_{ }^{ }\left(x^2+1\right)^2dx∫​(x2+1)2dx﻿ using substitution method

﻿x55+2x33+c\frac{x^5}{5}+\frac{2x^3}{3}+c5x5​+32x3​+c﻿

﻿2x33+x+c\frac{2x^3}{3}+x+c32x3​+x+c﻿

﻿x55+2x33+x+c\frac{x^5}{5}+\frac{2x^3}{3}+x+c5x5​+32x3​+x+c﻿

Determine the integral ﻿∫[sin⁡xx]dx\int_{ }^{ }\left[\frac{\sin x}{x}\right]dx∫​[xsinx​]dx﻿ using substitution method

﻿sec⁡2x2+c\frac{\sec^2x}{2}+c2sec2x​+c﻿

﻿sec⁡3x2+c\frac{\sec^3x}{2}+c2sec3x​+c﻿

﻿sec⁡4x2+c\frac{\sec^4x}{2}+c2sec4x​+c﻿

Determine the integral﻿∫[sin⁡xx]dx\int_{ }^{ }\left[\frac{\sin x}{x}\right]dx∫​[xsinx​]dx﻿ using substitution method

﻿sin⁡4x4+c\frac{\sin^4x}{4}+c4sin4x​+c﻿

﻿sec⁡3x2+c\frac{\sec^3x}{2}+c2sec3x​+c﻿

﻿sec⁡4x2+c\frac{\sec^4x}{2}+c2sec4x​+c﻿

Determine the integral ﻿∫[xcos⁡x]dx\int_{ }^{ }\left[x\cos x\right]dx∫​[xcosx]dx﻿ using substitution method

﻿−cos⁡x24+c-\frac{\cos x^2}{4}+c−4cosx2​+c﻿

﻿sin⁡x44+c\frac{\sin x^4}{4}+c4sinx4​+c﻿

﻿sin⁡4x4+c\frac{\sin^4x^{ }}{4}+c4sin4x​+c﻿

Determine the integral ﻿∫x(x2+1)100dx\int_{ }^{ }x\left(x^2+1\right)^{100}dx∫​x(x2+1)100dx﻿ using substitution method

﻿(x2+1)109109+c\frac{\left(x^2+1\right)^{109}}{109}+c109(x2+1)109​+c﻿

﻿−(x2+1)101202+c-\frac{\left(x^2+1\right)^{101}}{202}+c−202(x2+1)101​+c﻿

﻿−(x2+1)101119+c-\frac{\left(x^2+1\right)^{101}}{119}+c−119(x2+1)101​+c﻿

Determine the integral ﻿∫sin⁡(2x+1)dx\int_{ }^{ }\sin\left(2x+1\right)dx∫​sin(2x+1)dx﻿ using substitution method

﻿(2x+1)2+c\frac{\left(2x+1\right)}{2}+c2(2x+1)​+c﻿

﻿cos⁡(2x+1)2+c\frac{\cos\left(2x+1\right)}{2}+c2cos(2x+1)​+c﻿

﻿−cos⁡(2x+1)2+c\frac{-\cos\left(2x+1\right)}{2}+c2−cos(2x+1)​+c﻿

Determine the integral ﻿∫2x[sin⁡sin⁡x2]dx\int_{ }^{ }2x\left[\sin\sin x^2\right]dx∫​2x[sinsinx2]dx﻿ using substitution method

﻿−cos⁡x2+c-\cos x^2+c−cosx2+c﻿

﻿sin⁡x2+c\sin x^2+csinx2+c﻿

﻿sin⁡x+c\sin x+csinx+c﻿

Determine the integral﻿∫(1−x)9dx\int_{ }^{ }\left(1-x\right)^9dx∫​(1−x)9dx﻿ using substitution method

﻿−(1−x)910−cos⁡x2+c-\frac{\left(1-x\right)^9}{10}-\cos x^2+c−10(1−x)9​−cosx2+c﻿

﻿−(1−x)1010+c-\frac{\left(1-x\right)^{10}}{10}+c−10(1−x)10​+c﻿

﻿−(1−x)109+c-\frac{\left(1-x\right)^{10}}{9}+c−9(1−x)10​+c﻿

Determine the integral﻿∫(2x+1)3dx\int_{ }^{ }\left(2x+1\right)^3dx∫​(2x+1)3dx﻿ using substitution method

﻿(2x+1)38+c\frac{\left(2x+1\right)^3}{8}+c8(2x+1)3​+c﻿

﻿(2x+1)44+c\frac{\left(2x+1\right)^4}{4}+c4(2x+1)4​+c﻿

﻿(2x+1)48+c\frac{\left(2x+1\right)^4}{8}+c8(2x+1)4​+c﻿

Incorrect

Great!

Determine the integral $\int_{ }^{ }\left(ax+b\right)^ndx$ using substitution method

$\frac{\left(ax+b\right)^{n+1}}{an}+c$

$\frac{\left(ax+b\right)^n}{a\left(n+1\right)}+c$

$\frac{\left(ax+b\right)^{n+1}}{a\left(n+1\right)}+c$

Determine the integral $\int_{ }^{ }\left(x^2+1\right)^2dx$ using substitution method

$\frac{x^5}{5}+\frac{2x^3}{3}+c$

$\frac{2x^3}{3}+x+c$

$\frac{x^5}{5}+\frac{2x^3}{3}+x+c$

Determine the integral $\int_{ }^{ }\left[\frac{\sin x}{x}\right]dx$ using substitution method

$\frac{\sec^2x}{2}+c$

$\frac{\sec^3x}{2}+c$

$\frac{\sec^4x}{2}+c$

Determine the integral $\int_{ }^{ }\left[\frac{\sin x}{x}\right]dx$ using substitution method

$\frac{\sin^4x}{4}+c$

$\frac{\sec^3x}{2}+c$

$\frac{\sec^4x}{2}+c$

Determine the integral $\int_{ }^{ }\left[x\cos x\right]dx$ using substitution method

$-\frac{\cos x^2}{4}+c$

$\frac{\sin x^4}{4}+c$

$\frac{\sin^4x^{ }}{4}+c$

Determine the integral $\int_{ }^{ }x\left(x^2+1\right)^{100}dx$ using substitution method

$\frac{\left(x^2+1\right)^{109}}{109}+c$

$-\frac{\left(x^2+1\right)^{101}}{202}+c$

$-\frac{\left(x^2+1\right)^{101}}{119}+c$

Determine the integral $\int_{ }^{ }\sin\left(2x+1\right)dx$ using substitution method

$\frac{\left(2x+1\right)}{2}+c$

$\frac{\cos\left(2x+1\right)}{2}+c$

$\frac{-\cos\left(2x+1\right)}{2}+c$

Determine the integral $\int_{ }^{ }2x\left[\sin\sin x^2\right]dx$ using substitution method

$-\cos x^2+c$

$\sin x^2+c$

$\sin x+c$

Determine the integral $\int_{ }^{ }\left(1-x\right)^9dx$ using substitution method

$-\frac{\left(1-x\right)^9}{10}-\cos x^2+c$

$-\frac{\left(1-x\right)^{10}}{10}+c$

$-\frac{\left(1-x\right)^{10}}{9}+c$

Determine the integral $\int_{ }^{ }\left(2x+1\right)^3dx$ using substitution method

$\frac{\left(2x+1\right)^3}{8}+c$

$\frac{\left(2x+1\right)^4}{4}+c$

$\frac{\left(2x+1\right)^4}{8}+c$