By Christopher Thomas

Updated on Oct 1, 2011

To review these concepts, go to Integration by Substitution Study Guide.

**Integration by Substitution Practice Questions**

**Evaluate the following integrals.**

*x*^{4}(*x*^{5}+ 1)^{7}*dx*- (4
*x*+ 3)^{10}*dx* *x*^{2}(*x*^{3}– 1)^{4}*dx*- (
*x*^{3}– 9*x*+ 4)*dx* -
*x*√*x*2 – 1*dx* - 3√
*x**dx* - √3
*x*+ 4*dx* -
*dx* - 2
*x*^{3}cos(*x*^{4})*dx* -
*dx* - (8
*x*+ 5)(4*x*^{2}– + 5*x*– 1)^{3}*dx* -
*dx* -
*dx* - sin(
*x*)cos(*x*)*dx* - sin
^{2}(*x*)cos(*x*)*dx* - cos(4
*x*)*dx* - 4cos(
*x*)*dx* - sin(7
*x*– 2) dx *e*^{x}sin(*e*^{x})*dx*-
*dx* -
*dx* -
*xe*^{(x2)}*dx* - tan(
*x*)*dx*=*dx* -
*dx*

**Solutions**

- (
*x*^{5}+ 1)^{8}+*c* - (4
*x*+ 3)^{11}+*c* *x*^{4}–*x*^{2}+ 4*x*+*c*- (
*x*^{2}– 1)^{}+*c* - 14
- 26
- ln3
*x*^{3}– 5*x*+*c* - sin(
*x*^{4}) +*c* - √3
*x*4 – 2*x*+ 1 +*c* - (4
*x*^{2}+ 5*x*– 1)^{4}+*c* - – +
*c* - ln|4
*x*+ 101 +*c* - Using
*u*= sin(*x*), the solution is sin^{2}+*c*. Using = cos(*x*), the solution is – cos^{2}(*x*) +*c*. Because sin^{2}(*x*) + cos^{2}(*x*) = 1, these solutions will be the same if the second +*c*is greater than the first one. - sin
^{3}(*x*) +*c* - sin(4
*x*) +*c* - 4sin(
*x*) +*c* - –cos(7
*x*– 2) +*c* - –cos(
*e*^{x}) +*c* - (ln(
*x*))^{4}+*c* - ln|ln(
*x*)| +*c* *e*(*x*^{2}) +*c*- –ln(cos(
*x*)) +*c* - ln(1 +
*e*^{x}) +*c*

From Calculus Success in 20 Minutes A Day. Copyright © 2006 by LearningExpress, LLC. All Rights Reserved.

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