How do you integrate x * cos^2 (x)?

1 Answer
Narad T.
Nov 5, 2016

The answer is =x^2/4+(xsin2x)/4+(cos2x)/8+C

Explanation:

First replace cos^2x by 1/2(1+cos2x)
As cos2x=2cos^2x-1
:.intxcos^2xdx=1/2int(x+xcos2x)dx

=1/2*x^2/2+1/2intxcos2xdx

We integrate the last integral by parts
u=x=>u'=1
v'=cos2x=>v=(sin2x)/2
So intxcos2xdx=(xsin2x)/2-1/2intsin2xdx
=(xsin2x)/2+(cos2x)/4
Putting it all together

intxcos^2xdx=x^2/4+(xsin2x)/4+(cos2x)/8+C

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