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

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

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integral of (x^2cos(x))

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

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

Solution steps

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

Apply Integration By Parts

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

= 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

\int sin (\frac{n \cdot π}{3} x) d x

\int \frac{y}{1 + x y} d x

y = 1 - x^{2}, x = 2

\frac{x}{4 x + 8}

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