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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

Grade:12

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

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

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

 

Now you can easly intigrate


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Badiuddin
 

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