What is the integral of cos((mpix)/3) ?

The integral of cos((mpix)/3) is 3/(pim)sin((pimx)/3)+C

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integral of cos((mpix)/3)

\int cos (\frac{mπ x}{3}) d x

\frac{3}{πm} sin (\frac{πm x}{3}) + C

Solution steps

\int cos (\frac{mπ x}{3}) d x

Apply Integration By Parts

: x cos (\frac{πm x}{3}) - \int - \frac{πm}{3} x sin (\frac{πm x}{3}) d x

= x cos (\frac{πm x}{3}) - \int - \frac{πm}{3} x sin (\frac{πm x}{3}) d x

\int - \frac{πm}{3} x sin (\frac{πm x}{3}) d x = x cos (\frac{πm x}{3}) - \frac{3}{πm} sin (\frac{πm x}{3})

= x cos (\frac{πm x}{3}) - (x cos (\frac{πm x}{3}) - \frac{3}{πm} sin (\frac{πm x}{3}))

Simplify

= \frac{3}{πm} sin (\frac{πm x}{3})

Add a constant to the solution

= \frac{3}{πm} sin (\frac{πm x}{3}) + C

\frac{\partial}{\partial y} (2 y cos (x))

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (2 x)

x \to 0 + lim (e^{- \frac{5}{x}})

\int \frac{1}{- x ^{2} + 14 x + 50} d x

1 + sin^{2} (e^{5 x})

What is the integral of cos((mpix)/3) ?
The integral of cos((mpix)/3) is 3/(pim)sin((pimx)/3)+C