What is the integral of w^3sin(w) ?

The integral of w^3sin(w) is -w^3cos(w)+3(w^2sin(w)-2(-wcos(w)+sin(w)))+C

Popular >

integral of w^3sin(w)

\int w^{3} sin (w) d w

- w^{3} cos (w) + 3 (w^{2} sin (w) - 2 (- w cos (w) + sin (w))) + C

Solution steps

\int w^{3} sin (w) d w

Apply Integration By Parts

: - w^{3} cos (w) - \int - 3 w^{2} cos (w) d w

= - w^{3} cos (w) - \int - 3 w^{2} cos (w) d w

\int - 3 w^{2} cos (w) d w = - 3 (w^{2} sin (w) - 2 (- w cos (w) + sin (w)))

= - w^{3} cos (w) - (- 3 (w^{2} sin (w) - 2 (- w cos (w) + sin (w))))

Simplify

= - w^{3} cos (w) + 3 (w^{2} sin (w) - 2 (- w cos (w) + sin (w)))

Add a constant to the solution

= - w^{3} cos (w) + 3 (w^{2} sin (w) - 2 (- w cos (w) + sin (w))) + C

\int tan^{3} (3 x) sec^{6} (3 x) d x

\int \frac{1}{x 6 x - 1} d x

\int \frac{1}{x ^{2} - n} d x

\int x^{2} 4^{x^{3}} d x

\int 3 tan^{2} (x) sec^{4} (x) d x

What is the integral of w^3sin(w) ?
The integral of w^3sin(w) is -w^3cos(w)+3(w^2sin(w)-2(-wcos(w)+sin(w)))+C