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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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Using Integration Tables In Exercises 9–36, use the integration table in Appendix C to find the indefinite integral. See Examples 1, 2,3, and 5.

4 x 2 ln 2 x d x

To determine

To calculate: The solution of indefinite integral 4x2ln2xdx.

Explanation

Given Information:

The expression is provided as, 4x2ln2xdx.

Formula used:

The formula 43 for integral unlnudu is,

unlnudu=un+1(n+1)2[1+(n+1)lnu]+C

General power differentiation Rule,

ddx[un]=nun1dudx

Calculation:

Let u=2x.

Differentiate on both side with respect to x,

du=2dx

Consider the provided expression,

4x2ln2xdx

Multiply and divide by 2.

4x2ln2xdx=12(4x2ln2x)2dx=12((2x)2ln2x)2dx

Substitute u for 2x, and du for 2dx

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