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

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

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integral of sin(x)x^2

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

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

Solution steps

\int sin (x) x^{2} 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

\int_{1}^{100} x d x

y^{^{''}} - (\frac{6}{x}) y^{^{'}} - (\frac{8}{x ^{2}}) y = 0

x \to - 1 lim (\frac{x ^{2} + 5}{x + 1})

\int (x + 14) 28 x + x^{2} d x

\int cos^{2} (6 x) d x

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