What is the integral of 7x^2sin(pix) ?

The integral of 7x^2sin(pix) is 7(-1/pi x^2cos(pix)+2/pi (1/pi xsin(pix)+1/(pi^2)cos(pix)))+C

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integral of 7x^2sin(pix)

\int 7 x^{2} sin (π x) d x

7 (- \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 7 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

= 7 \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

= 7 (- \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))

= 7 (- \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

= 7 (- \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

= 7 (- \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 y}{d x} = \frac{1}{y - x}

\int x^{2} - 4 x + 7 d x

x \to - 1 lim (\frac{x ^{2} - 3}{1 - x})

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

\int \frac{7}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

What is the integral of 7x^2sin(pix) ?
The integral of 7x^2sin(pix) is 7(-1/pi x^2cos(pix)+2/pi (1/pi xsin(pix)+1/(pi^2)cos(pix)))+C