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Question

Solve cosxsinx1+sin2xdx

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Solution

Solve the given trigonometric function.

=cosxsinx1+sin2xdx

=cosxsinxsin2x+cos2x+2sinxcosxdx

=cosxsinx(cosx+sinx)2dx

Let cosx+sinx=t

Then,

ddx(cosx+sinx)=ddxt

sinx+cosx=dtdx

(cosxsinx)dx=dt

Now,

dtt2

=t2dt

=t2+12+1

=1t=1cosx+sinx

Hence, this is the answer.


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