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

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Grade 12Algebra

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

harshit agarwal

16 Years agoGrade 12

1 Answer

Badiuddin askIITians.ismu Expert

16 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(e^x)=1/(1+e^x)

Now you can easly intigrate

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