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

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

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integral of cos(x)*x^2

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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