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Solve the integral: xsinx2dx.

Short Answer

Expert verified

The required answer is-cosx22+c.

Step by step solution

01

Step 1. Given information. 

We have given integral isxsinx2dx.

02

Step 2. Solve the integration by parts . 

We have, u=xdu=dx

and

dv=sin2xdxv=sin2xdxv=x2-sin2x4

The formula of integration by parts is udv=uv-vdu

xsinx2dx=xx2-sin2x4-x2-sin2x4dx=x22-xsin2x4-x24+sin2x4dx=-cosx22+c

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