Integration by Parts with Power Reduction - Confirming Solution

[nameVoid]

Homework Statement

I(xsin^2x,x)
(1/2)I(x(1-cos2x),x)
(1/2)I(x,x)-(1/2)I(xcos2x,x)
x^2/4-(1/2)I(xcos2x,x)
u=x du=dx
dv=cos2x v=sin2x/2
x^2/4-xsin2x/4+I(sin2x,x)/4
x^2/4-xsin2x/4-cos2x/8+C
book is showing a diffrent solution from integrating by parts before power reduction
can someone please confirm

Homework Equations

The Attempt at a Solution

 

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Your answer is correct.