What is the integral of 4x^2sin(x) ?

The integral of 4x^2sin(x) is 4(-x^2cos(x)+2(xsin(x)+cos(x)))+C

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integral of 4x^2sin(x)

\int 4 x^{2} sin (x) d x

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

Solution steps

\int 4 x^{2} sin (x) d x

Take the constant out:

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

= 4 \cdot \int x^{2} sin (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

y = 2 x, (8, 4)

\frac{\partial}{\partial y} ((x + 2) y)

\frac{\partial}{\partial x} (ln (\frac{x}{2}))

\frac{d}{d x} (7 ln (x))

\frac{d y}{d x} = 2^{4 x - y}

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