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

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

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integral of 3x^2sin(pix)

\int 3 x^{2} sin (π x) d x

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

Solution steps

\int 3 x^{2} sin (π x) d x

Take the constant out:

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

= 3 \cdot \int x^{2} sin (π x) d x

Apply Integration By Parts

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

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

\int - \frac{2}{π} x cos (π x) d x = - \frac{2}{π} (\frac{1}{π} x sin (π x) + \frac{1}{π ^{2}} cos (π x))

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d y} (\frac{y}{5})

t \to 0 lim (\frac{t ^{2} + 3 t}{t})

\frac{d}{d x} ((8 x + e^{- x^{2}})^{2})

\frac{d}{d x} (x + \frac{100}{x})

(2 y^{2} + 4 x^{2}) d x - x y d y = 0

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