What is the integral of x(-sin(x)) ?

The integral of x(-sin(x)) is xcos(x)-sin(x)+C

Popular >

integral of x(-sin(x))

\int x (- sin (x)) d x

x cos (x) - sin (x) + C

Solution steps

\int x (- sin (x)) d x

Apply Integration By Parts

: - \frac{1}{2} x^{2} sin (x) - \int - \frac{1}{2} x^{2} cos (x) d x

= - \frac{1}{2} x^{2} sin (x) - \int - \frac{1}{2} x^{2} cos (x) d x

\int - \frac{1}{2} x^{2} cos (x) d x = - \frac{1}{2} x^{2} sin (x) - x cos (x) + sin (x)

= - \frac{1}{2} x^{2} sin (x) - (- \frac{1}{2} x^{2} sin (x) - x cos (x) + sin (x))

Simplify

- \frac{1}{2} x^{2} sin (x) - (- \frac{1}{2} x^{2} sin (x) - x cos (x) + sin (x)) : x cos (x) - sin (x)

= x cos (x) - sin (x)

Add a constant to the solution

= x cos (x) - sin (x) + C

\int sin^{7} (\frac{x}{6}) cos (\frac{x}{6}) d x

\int 4 x^{2} e^{- x^{2}} d x

\frac{3}{x ^{2}}

\int (\frac{7 + x + x}{x}) d x

\int - 4 x^{3} cos (- 4 x) d x

What is the integral of x(-sin(x)) ?
The integral of x(-sin(x)) is xcos(x)-sin(x)+C