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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.

1 2 x 2 ( 2 x 1 ) 2 d x

To determine

To calculate: The solution of indefinite integral 12x2(2x1)2dx.

Explanation

Given Information:

The expression is provided as, 12x2(2x1)2dx.

Formula used:

The formula 13 for integral 1u2(a+bu)2du is,

1u2(a+bu)2du=1a2(a+2buu(a+bu)+2baln|ua+bu|)+C

Calculation:

Let u=x.

Differentiate both side of the above function,

du=dx

Consider the provided expression,

12x2(2x1)2dx

Rewrite.

12x2(2x1)2dx=121x2(1+2x)2dx

Here, a=1, b=2, u=x and du=dx.

Substitute u for x, a for 1, b for 2, and du for dx

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