How to integrate xcos2(x2)dx ?

xcos2(x2)dx

3 Answers
Apr 18, 2018

see below

Explanation:

We have, xcos2(x2)dx
Substituting x2 as y,we get,
2xdx=dy
Putting this value in the main integral,we get,
12dycosy
Or, 12secy dy
Or,lntanx2+secx22+C

Apr 18, 2018

xcos2(x2)dx=tanx22+C

Explanation:

xcos2(x2)dx=

=121cos2(x2)(2x)dx=

=[121cos2(t)dt]t=x2=

=[12tant+C]t=x2=

=tanx22+C

Apr 18, 2018

The integral is equal to 12tan(x2)+C

Explanation:

Let u=x2. Then du=2xdx and dx=du2x

I=12cos2udu

I=12sec2udu

This is a known integral

I=12tanu+C

Reverse the substitution

I=12tan(x2)+C

Hopefully this helps!