Question

Question #1c46e

Answer 1

Trisha - integrate by parts twice ...

Explanation:

`u=sin(lnx)`

`du=[cos(lnx)]/x dx`

`dv=x dx`

`v=x^2/2`

Now, using integration by parts ...

`int xsin(lnx) dx=(x^2/2)(sin(lnx))-int(xcos(lnx))/2 dx`

Do it again on the integral ...

`u=cos(lnx)/2`

`du=-[sin(lnx)]/(2x) dx`

`dv=x dx`

`v=x^2/2`

Using the integration by parts formula one more time ...

`int xsin(lnx) dx=(x^2/2)(sin(lnx))-x^2cos(lnx)/4-1/4(intxsin(lnx))`

Combine integral terms ...

`(5/4)int xsin(lnx) dx=(x^2/2)(sin(lnx))-x^2cos(lnx)/4`

Simplify ...

`int xsin(lnx) dx=-x^2/5[cos(lnx)-2sin(lnx)]+C`

hope that helped