`intsin^(3)xdx=?`

Options

A. `-(3)/(4)"cos"x+(cos3x)/(12)+C`
B. `(3)/(4)cosx+(cos3x)/(12)+C`
C. `-(3)/(4)cosx-(cos3x)/(12)+C`
D. none of these

Answer

A

Explanation

`sin3x=3sinx-4sin^(3)xrArrsin^(3)x=-(1)/(4)(3sinx-sin3x)`.
`:." "intsin^(3)xdx=(3)/(4)intsinxdx-(1)/(4)intsin3xdx`
`=(3)/(4)(-cosx)-(1)/(4)((-cos3x))/(3)+C=(cos3x)/(12)-(3)/(4)cosx+C`.