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

\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} (x^{\frac{2}{3}} + y^{\frac{2}{3}})

\frac{d}{d x} (- tan (x^{2}))

\int \frac{1}{ln ( x ^{2} )} d x

n = 1 \sum \infty \frac{3 ^{n}}{5 ^{n}}

x \to 0 lim (\frac{9 + x}{x ^{3}})

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