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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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Checkpoint 7 Worked-out solution available at LarsonAppliedCalculus.com

Find x x 2 + 4

dx by the method of substitution.

To determine

To calculate: The value of the provided indefinite integral xx2+4dx.

Explanation

Given Information:

The provided indefinite integral is xx2+4dx.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

undu=un+1n+1+C,

where n1

Calculation:

Consider the indefinite integral say I,

I=xx2+4dx

Multiply and divide by 2 in the right-hand side of above integral

I=(12)xx2+4(2)dx

Take the factor 12 out of the integrand

I=12xx2+4(2)dx

Or

I=12x2+4(2x)dx

Let

x2+4=u … (1)

Differentiate the above equation with respect to x

ddx(x2+4)=

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