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Evaluate int sin(logx)dx....

Evaluate `int sin(logx)dx`.

A

`(1)/(2)xsinlogx+(1)/(2)xcos(logx)+C`

B

`(1)/(2)xsinlogx-(1)/(2)xcos(logx)+C`

C

`-(1)/(2)xsin(logx)+(1)/(2)xcos(logx)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int{sinunderset(I)((logx))*underset(II)1}dx=(sinlogx)x-int(cos(logx))/(x)*xdx`
`=xsin(logx)-int{cosunderset(I)((logx))*underset(II)(1)}dx`
`=xsin(logx)-cos(logx)*x+int(-sin(logx))/(x)*xdx`
`:." "2I=xsin(logx)-xcos(logx)-C`
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