What is the integral of q^2cos(2q) ?

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

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integral of q^2cos(2q)

\int q^{2} cos (2 q) d q

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

Solution steps

\int q^{2} cos (2 q) d q

Apply Integration By Parts

: \frac{1}{2} q^{2} sin (2 q) - \int q sin (2 q) d q

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

\int q sin (2 q) d q = - \frac{1}{2} q cos (2 q) + \frac{1}{4} sin (2 q)

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

Simplify

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

Add a constant to the solution

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

x d x + y d y = 0

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

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

4 x (x^{2} - 4)

\frac{\partial}{\partial x} (7 y - y^{3} - 4 x^{2} y)

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