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

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

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integral of x^2*sin(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

y^{^{'}} - \frac{y}{x} = 2

y^{^{''}} - 7 y^{^{'}} + 2 y = t e^{t}

\frac{\partial}{\partial x} (x^{2} + e^{x y})

\int 6 x^{8} (x^{9} + 3)^{5} d x

\int \frac{e ^{4 x}}{e ^{4 x} + 5} d x

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