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

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

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integral of x^2sin(x)

\int x^{2} 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

\frac{d}{d x} (2 x (sin (x) + cos (x)))

\int \frac{x ^{2} + 4}{x + 2} d x

\int \frac{e ^{x}}{1 + 36 e ^{2 x}} d x

\frac{5}{3} x^{3} - \frac{5}{2} x^{2}

\frac{4 x ^{2} + 4 x + 8}{x}

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