   Chapter 5.2, Problem 36E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Integration by Substitution In Exercises 35–42, use the method of substitution to find the indefinite integral. Check your result by differentiating. See Examples 6 and 7. ∫ ( 5 x − 3 ) 2 / 3 d x

To determine

To calculate: The indefinite integral of (5x3)23 dx and to check the result by differentiating.

Explanation

Given Information:

The provided expression is, (5x3)23 dx.

Formula used:

General Power Rule:

If u is a differentiable function of x, then

undudxdx=undu=un+1n+1+c,n1

The Constant Multiple Rule:

ddxcf(x)=cf(x)

The Chain Rule:

ddxf(g(x))=f(g(x))g(x)

The Power Rule:

ddxxn=nxn1

Where n is a real number.

Calculation:

Consider the expression, (5x3)23 dx,

Let u=5x3,

So,

du=5dxdudx=15

Now use the general power rule to get,

15(u)23du

Now the integral will be:

15.u23+123+1+C=15u5353+C=1535u53+C=325u53+C

Substitute back the value of u to get,

(

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