   Chapter 5.2, Problem 35E ### 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. ∫ 4 x + 3 3   d x

To determine

To calculate: The indefinite integral of 4x+33 dx and to check the result by differentiating.

Explanation

Given Information:

The provided expression is 4x+33 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 4x+33 dx,

This can be written as (4x+3)13dx.

Let u=4x+3,

So,

du=4dxdudx=4

Now use the general power rule to get,

14(u)13du

Now the integral will be:

14.u13+113+1+c=14.u4343+C=14

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