What is the integral of xsin(-x) ?

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

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integral of xsin(-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

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

Simplify

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

= x cos (x) - sin (x)

Add a constant to the solution

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

\frac{s + 1}{s ^{2} + s - 1}

x \to 0 lim (\frac{1}{2} + e^{\frac{1}{x}})

\frac{d}{d x} (x (x - 2)^{\frac{2}{3}})

\frac{d}{d x} (\frac{2 x}{2 x - 1})

\int x^{5} e x^{6} + 1 d x