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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)/(5 sqrt(15)),f(x) = (4 tan ""x+3)/(sqrt(15))`

B

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

Text Solution

Verified by Experts

The correct Answer is:
D
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