Chapter 4.5, Problem 15E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding an Indefinite Integral In Exercises 9-30, find the indefinite integral and check the result by differentiation. ∫ x 2 ( 2 x 3 − 1 ) 4   d x

To determine

To Calculate: The indefinite integral x2(2x31)4dx and verify it by differentiation.

Explanation

Given:

The integral âˆ«x2(2x3âˆ’1)4dx.

Formula used:

According to theorem for change of variable for indefinite integrals,

If u=g(x) then du=g'(x)

Then integral will take the following form:

âˆ«f(g(x))g'(x)dx=âˆ«f(u)du=F(u)+C

Calculation:

Consider, u=2x3âˆ’1.

Then, differentiate above equation with respect to x:

dudx=(2(3x2)âˆ’0)du=(6x2)dxdu6=x2dx

So, convert integral in terms of u,

âˆ«x2(2x3âˆ’1)4dx=âˆ«u4du<

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