2f(tan 2 x)+3f(cot 2 x) =3sin 2 x + 2cos 2 x. Find ∫f(e x )dx (limit 0 to ln tan α

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


1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

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


so f(ex)=1/(1+ex)


Now you can easly intigrate

Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE preparation. All the best harshit


Askiitians Experts


Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy


Get your questions answered by the expert for free