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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.

8 x 2 ( 9 2 x ) 5 d x

To determine

To calculate: The solution of indefinite integral 8x2(92x)5dx.

Explanation

Given Information:

The expression is provided as, 8x2(92x)5dx.

Formula used:

The formula for integral u2(a+bu)ndu is,

u2(a+bu)ndu=1b3(1(n3)(a+bu)n3+2a(n2)(a+bu)n2a2(n1)(a+bu)n1)+C

Calculation:

Let u=x.

Differentiate the above integral with respect to x,

du=dx

Consider the provided expression:

8x2(92x)5dx

Rewrite.

8x2(92x)5dx=8x2(9+(2)x)5dx

Here, a=9, b=2, n=5, u=x and du=dx.

Substitute u for x, a for 9, b for 2, n for 5, and du for dx.

8x2(92x)5dx=8u2(a+bu)ndx

Use the integral formula to solve the above integral as,

8x2(92x)5dx=8[1b3(1(n3)(a+bu)n3+2a(n2)(a+bu)n2a2(n1)(a+bu)n1)]+C

Substitute x for u, 9 for a, 5 for n, and 2 for b

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