What is the integral of (-6x^2+2x)sin(x) ?

The integral of (-6x^2+2x)sin(x) is -6(-x^2cos(x)+2(xsin(x)+cos(x)))+2(-xcos(x)+sin(x))+C

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integral of (-6x^2+2x)sin(x)

\int (- 6 x^{2} + 2 x) sin (x) d x

- 6 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + 2 (- x cos (x) + sin (x)) + C

Solution steps

\int (- 6 x^{2} + 2 x) sin (x) d x

Expand

(- 6 x^{2} + 2 x) sin (x) : - 6 x^{2} sin (x) + 2 x sin (x)

= \int - 6 x^{2} sin (x) + 2 x sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 6 x^{2} sin (x) d x + \int 2 x sin (x) d x

\int 6 x^{2} sin (x) d x = 6 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))

\int 2 x sin (x) d x = 2 (- x cos (x) + sin (x))

= - 6 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + 2 (- x cos (x) + sin (x))

Add a constant to the solution

= - 6 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + 2 (- x cos (x) + sin (x)) + C

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What is the integral of (-6x^2+2x)sin(x) ?
The integral of (-6x^2+2x)sin(x) is -6(-x^2cos(x)+2(xsin(x)+cos(x)))+2(-xcos(x)+sin(x))+C