What is the integral of cos(xn) ?

The integral of cos(xn) is 1/n sin(xn)+C

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integral of cos(xn)

\int cos (x n) d x

\frac{1}{n} sin (x n) + C

Solution steps

\int cos (x n) d x

Apply u-substitution

: \int \frac{cos ( u )}{n} d u

= \int \frac{cos ( u )}{n} d u

Take the constant out:

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

= \frac{1}{n} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{n} sin (u)

Substitute back

u = x n

= \frac{1}{n} sin (x n)

Add a constant to the solution

= \frac{1}{n} sin (x n) + C

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