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int x sinx sec^(3)x dx is equal to...

`int x sinx sec^(3)x dx` is equal to

A

`(1)/(2)[ sec^(2)x-tanx]+c`

B

`(1)/(2)[x sec^(2)x-tanx]+c`

C

`(1)/(2)[x sec^(2)x+tanx]+c`

D

`(1)/(2)[ sec^(2)x+tanx]+c`

Text Solution

Verified by Experts

The correct Answer is:
B
`intx sinx sec^(3)x dx=intx sinx(1)/(cos^(3)x)dx`
`=int x tanx sec^(2)x dx `
`=x int secx(secx tanx)dx-int[int secx(secx tanx)dx]dx+C`
`=x(sec^(2)x)/(2)-int(sec^(2)x)/(2)dx+C`
`=x(sec^(2)x)/(2)-(tanx)/(2)+C`
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