   Chapter 4.5, Problem 53E

Chapter
Section
Textbook Problem

Change of Variables In Exercises 53-60, find the indefinite integral by making a change of variables. ∫ x x + 6   d x

To determine

To calculate: The indefinite integral xx+6dx.

Explanation

Given:

The provided integral is:

xx+6dx

Formula used:

The power rule for integration is:

xndx=xn+1n+1+c,  n1

Calculation:

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

Consider, u=x+6. Therefore, u6=x.

Differentiate above equation with respect to x:

dudx=(1+0)du=dx

Put x+6=u, x=u6 and dx=du in the provided equation:

xx+6dx=(u6)udu=(u326u)du=u32du6udu=

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