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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \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)))

Simplify

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

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

Add a constant to the solution

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

\frac{2 a + b}{( s + 1 )}

\int 20 + 75 e^{- \frac{x}{50}} d x

5 x^{2}

n = 1 \sum \infty (- 3)^{3 n - 1}

\frac{d}{d x} (ln (\frac{x ^{3} + 1}{x ^{2} + 1}))

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