What is the integral of x^2sin(3x) ?

The integral of x^2sin(3x) is -1/3 x^2cos(3x)+2/27 (3xsin(3x)+cos(3x))+C

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integral of x^2sin(3x)

\int x^{2} sin (3 x) d x

- \frac{1}{3} x^{2} cos (3 x) + \frac{2}{27} (3 x sin (3 x) + cos (3 x)) + C

Solution steps

\int x^{2} sin (3 x) d x

Apply Integration By Parts

: - \frac{1}{3} x^{2} cos (3 x) - \int - \frac{2}{3} x cos (3 x) d x

= - \frac{1}{3} x^{2} cos (3 x) - \int - \frac{2}{3} x cos (3 x) d x

\int - \frac{2}{3} x cos (3 x) d x = - \frac{2}{27} (3 x sin (3 x) + cos (3 x))

= - \frac{1}{3} x^{2} cos (3 x) - (- \frac{2}{27} (3 x sin (3 x) + cos (3 x)))

Simplify

= - \frac{1}{3} x^{2} cos (3 x) + \frac{2}{27} (3 x sin (3 x) + cos (3 x))

Add a constant to the solution

= - \frac{1}{3} x^{2} cos (3 x) + \frac{2}{27} (3 x sin (3 x) + cos (3 x)) + C

\frac{d y}{d x} = tan^{2} (x)

\frac{d ^{2}}{d x ^{2}} (\frac{3 x + 4}{2 x - 5})

\int \frac{1}{( cos ( x ) ) ^{2}} d x

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

y = 3 (x + 1), y = 4 (x + 1), x = 3

What is the integral of x^2sin(3x) ?
The integral of x^2sin(3x) is -1/3 x^2cos(3x)+2/27 (3xsin(3x)+cos(3x))+C