What is the integral of cos(n*x) ?

The integral of cos(n*x) is 1/n sin(nx)+C

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integral of cos(n*x)

\int cos (n \cdot x) d x

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

Solution steps

\int cos (n x) 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 = n x

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{1}{( 2 n + 1 ) ^{3}}

\int \frac{1}{x ^{4} + 4 x ^{2} + 4} d x

ln (w (h - l) + π - T) + ln (l)

\frac{\partial}{\partial x} (x^{2} + 3 x y)