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If the integral int(5tanx)/(tanx-2)dx=x+...

If the integral `int(5tanx)/(tanx-2)dx=x+aInabs(sinx-2cosx)+k`, then a is equal to

A

-1

B

-2

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
` int(5tanx)/(tanx-2)dx=int(5sinx)/(sinx-2cosx)dx`
`=int((sinx-2cosx)+2(cosx+2sinx))/((sinx-2cosx))dx`
`=int dx+2int(cosx+2sinx)/(sinx-2cosx)dx`
`=x+2 " In"|(sinx-2cosx)|+k`
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