What is the integral of (-x^2cos(x))/4 ?

The integral of (-x^2cos(x))/4 is -1/4 (x^2sin(x)-2(-xcos(x)+sin(x)))+C

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integral of (-x^2cos(x))/4

\int \frac{- x ^{2} cos ( x )}{4} d x

- \frac{1}{4} (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + C

Solution steps

\int \frac{- x ^{2} cos ( x )}{4} d x

Take the constant out:

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

= \frac{- 1}{4} \cdot \int x^{2} cos (x) d x

Simplify

= (- \frac{1}{4}) \cdot \int x^{2} cos (x) d x

Apply Integration By Parts

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

= (- \frac{1}{4}) (x^{2} sin (x) - \int 2 x sin (x) d x)

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

= (- \frac{1}{4}) (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

Simplify

= - \frac{1}{4} (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

Add a constant to the solution

= - \frac{1}{4} (x^{2} sin (x) - 2 (- x cos (x) + sin (x))) + C

\frac{\partial}{\partial x} (ln (x^{3} + y^{2}) - z)

y = x^{8 x}

\frac{\partial}{\partial x} (e^{s i n (x + y)})

f (x) = \frac{( x + 1 )}{( x - 1 )}

What is the integral of (-x^2cos(x))/4 ?
The integral of (-x^2cos(x))/4 is -1/4 (x^2sin(x)-2(-xcos(x)+sin(x)))+C