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If int(1)/((sinx+4)(sinx-1))dx =A(1)/(...

If `int(1)/((sinx+4)(sinx-1))dx`
`=A(1)/("tan"(x)/(2)-1)+B"tan"^(-1){f(x)}+C`. Then,

A

`A = (1)/(5), B = (-2)/(5sqrt(15)), f(x) = (4 tan x + 3)/(sqrt(15))`

B

`A = - (1)/(5), B tan^(-1), B = (1)/(sqrt(15)), f(x) = ( 4 tan ((x)/(2)) + 1)/(sqrt(15))`

C

`A = (2)/(5), B = (-2)/(5),f(x) = (4 tan x + 1)/(5)`

D

`A = (2)/(5),B = (-2)/(5sqrt(15)), f(x) = (4 tan (x)/(2) + 1)/(sqrt(15))`

Text Solution

Verified by Experts

The correct Answer is:
D
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