Question

How do you find the integral of `[ (1+cos^2(x)) / sin(x) ] dx`?

Answer 1

`-2ln|cscx +cotx| +cos x +C`

Explanation:

Rewrite the integrand as `[(1+1-sin^2 x)/sinx]= [(2-sin^2 x)/sinx]=2cscx -sinx`

Now `int csc x dx= -ln|csc x+cotx|` and `int sinx dx= -cos x`

The required Integral would be `-2ln|cscx +cotx| +cos x +C`