What is the integral of-2xsin(-x) ?

The integral of-2xsin(-x) is -2(xcos(x)-sin(x))+C

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integral of-2xsin(-x)

\int - 2 x sin (- x) d x

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

Solution steps

\int - 2 x sin (- x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \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)

= - 2 (- \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)

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

Expand

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

= - 2 (x cos (x) - sin (x))

Add a constant to the solution

= - 2 (x cos (x) - sin (x)) + C

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What is the integral of-2xsin(-x) ?
The integral of-2xsin(-x) is -2(xcos(x)-sin(x))+C