   Chapter 4.5, Problem 22E

Chapter
Section
Textbook Problem

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

To determine

To calculate: The indefinite integral x3(1+x4)2dx and verify it by differentiation.

Explanation

Given: The integral x3(1+x4)2dx.

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=1+x4.

Then, differentiate above equation with respect to x

dudx=(4x3)du=(4x3)dxdu4=x3dx

So, convert integral in terms of u,

x3(1+x4)2dx=

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