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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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In Exercises 1–6, use integration by parts to find the indefinite integral.

x ln x d x

To determine

To calculate: The solution of indefinite integral xlnxdx by the use of integration by parts.

Explanation

Given Information:

The provided expression is, xlnxdx.

Formula used:

The formula for integration by parts is,

udv=uvvdu

Here, u and v be the differentiable functions x.

General Power Integral Rule,

undu=un+1n+1+C

Calculation:

Consider the provided expression:

xlnxdx

Rewrite.

xlnxdx=xln(x)1/2dx=12xlnxdx=12xlnxdx

Let u=lnx and dv=xdx. So,

du=1xdx

And,

v=xdx=x22

Apply integration by parts to solve integral of 12xlnxdx

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