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inte^(x)(1-cotx+cot^(2)x)dx=...

`inte^(x)(1-cotx+cot^(2)x)dx=`

A

`e^(x)cotx+C`

B

`e^(x)"cosec x"+C`

C

`-e^(x)cotx+C`

D

`-e^(x)"cosec x"+C`

Text Solution

Verified by Experts

The correct Answer is:
C
`inte^(x)(1-cot x+cot^(2)x)dx`
`=int e^(x)(-cot x+"cosec"^(2)x)dx`
`=-int e^(x) cot x dx +int e^(x)" cosec"^(2)xdx`
On integration by parts, we get
`-e^(x) cot x - int e^(x)" cosec"^(2) x dx +int e^(x)"cosec"^(2) dx`
`=-e^(x)cotx+C`
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