   Chapter 4.5, Problem 14E

Chapter
Section
Textbook Problem

Finding an Indefinite Integral In Exercises 9-30, find the indefinite integral and check the result by differentiation. ∫ x 2 ( 6 − x 3 ) 5   d x

To determine

To calculate: The indefinite integral x2(6x3)5dx and verify it by differentiation.

Explanation

Given:

The integral x2(6x3)5dx.

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:

f(g(x))g'(x)dx=f(u)du=F(u)+C

Calculation:

Consider, u=6x3.

Then, differentiate above equation with respect to x:

dudx=(03x2)du=(3x2)dxdu3=x2dx

So, convert integral in terms of u,

x2(6x3)5dx=u5du3=

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