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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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.

3 2 x + 1 d x

To determine

To calculate: The indefinite integral of 32x+1dx and to check the result by differentiating.

Explanation

Given Information:

The provided expression is, 32x+1dx.

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 32x+1dx,

This can be written as 3(2x+1)12dx.

Let u=2x+1,

So,

du=2dxdu2=dx

Now use the general power rule to get,

32(u)12du

Now the integral will be:

32u12+112+1+C=32u12

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