Q .     The value of the indefinite integral `∫(cos^3x + cos^5x)/(sin^2x + sin^4x) dx` is

JEE 1995
A

`sin x – 2 (sin x)^(-1) + 5tan^(-1) (sin x) + c`

B

`sin x – 2 (sin x)^(-1) + c`

C

`sin x – 2 (sin x)^(-1) – 6tan^(-1) (sin x) + c`

D

`sin x – 6tan^(-1) (sin x) + c`

HINT

`I = ∫(cos^3x + cos^5x)/(sin^2x + sin^4x) dx` `= ∫((cos^2x + cos^4x).cosx dx)/((sin^2x + sin^4x))` Putting `sin x = t` & solve it.

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