What is the integral of tcos(pit) ?

The integral of tcos(pit) is 1/pi tsin(pit)+1/(pi^2)cos(pit)+C

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integral of tcos(pit)

\int t cos (π t) d t

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

Solution steps

\int t cos (π t) d t

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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What is the integral of tcos(pit) ?
The integral of tcos(pit) is 1/pi tsin(pit)+1/(pi^2)cos(pit)+C