Question
Asked Dec 3, 2019
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Use integration by parts to find the integral. (Use C for the constant of integration.)

 

x" In(ax) dx (a 0, n -1)
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x" In(ax) dx (a 0, n -1)

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Expert Answer

Step 1

Choose U and dv/dx as per LIATE rule.

Hence,

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du 1 1 u In(ax ах dv = x" dx n+1

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Step 2

The formula for integration by parts is given as;

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dv du 1 dx - j

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Step 3

Use the formula given in step 2 and the substitutions gi...

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Given integral; Isx" In(ax) dc It is expressed in the formula for parts as; I-In(ax) n1x 1 "dx In(ax) п+1 п+1 1 +C п+1 п+1( п+1 In(ax) In(ax) n+1 (n1) +C

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Tagged in

Math

Calculus

Integration