What is the integral of xcos(pi*x) ?

The integral of xcos(pi*x) is 1/pi xsin(pix)+1/(pi^2)cos(pix)+C

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integral of xcos(pi*x)

\int x cos (π \cdot x) d x

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

Solution steps

\int x cos (π x) d x

Apply Integration By Parts

: \frac{1}{π} x sin (π x) - \int \frac{1}{π} sin (π x) d x

= \frac{1}{π} x sin (π x) - \int \frac{1}{π} sin (π x) d x

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

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

Simplify

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

Add a constant to the solution

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

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

x \to 2 lim (\frac{x ^{2} - 6}{x - 3})

\frac{d}{d x} (1 + ln^{2} (x))

\frac{\partial}{\partial x} (tan (2 x))

\int_{0}^{1} 2 π x (x - x^{3}) d x

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