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The value of int("cosec x")/(cos^(2)(1+l...

The value of `int("cosec x")/(cos^(2)(1+logtan.(x)/(2)))dx` is

A

`-tan(1+logtan.(x)/(2))+c`

B

`sec^(2)(1+logtan.(x)/(2))+c`

C

`tan(1+log tan.(x)/(2))+c`

D

`sin^(2)(1+logtan.(x)/(2))+c`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int("cosec x")/((cos^2)(1+log tan.(x)/(2)))dx`
`"Let "1+log tan.(x)/(2)=t`
`therefore" "(1)/(sin x)dx=dt`
`therefore" "I=int(dt)/(cos^(2)t)`
`" "=tant+c`
`" "=tan(1+log tan.(x)/(2))+c`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-Single Correct Answer Type
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