What is the integral of cos(nxpi) ?

The integral of cos(nxpi) is 1/(pin)sin(nxpi)+C

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integral of cos(nxpi)

\int cos (n x π) d x

\frac{1}{πn} sin (n x π) + C

Solution steps

\int cos (n x π) d x

Apply u-substitution

: \int \frac{cos ( u )}{πn} d u

= \int \frac{cos ( u )}{πn} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{πn} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{πn} sin (u)

Substitute back

u = n x π

= \frac{1}{πn} sin (n x π)

Add a constant to the solution

= \frac{1}{πn} sin (n x π) + C

f (x) = \frac{x + 6}{x - 6}

(1 - x) e^{x + \frac{x ^{2}}{2}}

x \to 0 + lim (- x^{2} ln (6 x^{3}))

\int \frac{6}{5 + 6 x} d x

\int e^{x} 2 d x

What is the integral of cos(nxpi) ?
The integral of cos(nxpi) is 1/(pin)sin(nxpi)+C