What is the integral of (x^2cos(x)-2xcos(x)) ?

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

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integral of (x^2cos(x)-2xcos(x))

\int (x^{2} cos (x) - 2 x cos (x)) d x

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

Solution steps

\int x^{2} cos (x) - 2 x cos (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 x^{2} cos (x) d x - \int 2 x cos (x) d x

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

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

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

Add a constant to the solution

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

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