What is the integral of 13x^2sin(pix) ?

The integral of 13x^2sin(pix) is 13(-1/pi x^2cos(pix)+2/pi (1/pi xsin(pix)+1/(pi^2)cos(pix)))+C

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integral of 13x^2sin(pix)

\int 13 x^{2} sin (π x) d x

13 (- \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 13 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

= 13 \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

= 13 (- \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))

= 13 (- \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

= 13 (- \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

= 13 (- \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

y = 10 x - x + 3, (100, 3)

\int_{0}^{10} 2 π y (100 - y^{2}) d y

\int x^{2} 0. 4^{- x} x d x

(4, 5), (1, - 3)

t^{2} y^{^{''}} - 11 t y^{^{'}} + 35 y = 0

What is the integral of 13x^2sin(pix) ?
The integral of 13x^2sin(pix) is 13(-1/pi x^2cos(pix)+2/pi (1/pi xsin(pix)+1/(pi^2)cos(pix)))+C