2f(tan2x)+3f(cot2x) =3sin2x + 2cos2x. Find ∫f(ex)dx (limit 0 to ln tan α

HI harshit

2f(tan²x)+3f(cot²x) =3sin²x + 2cos²x

or  2f(tan²x)+3f(1/tan²x) =(3tan²x + 2)/(1+tan²x)

0r  2f(tan²x)+3f(1/tan²x) =2/(1+tan²x)  + 3tan²x/(1+tan²x)

 let y=tan²x

2f(y)+3f(1/y) =2/(1+y)  + 3/(1+1/y)

compairing we can say

f(y)=1/(1+y)

so f(e^x)=1/(1+e^x)

Now you can easly intigrate