What is the integral of cos(ax) ?

The integral of cos(ax) is 1/a sin(ax)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(ax)

\int cos (a x) d x

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

Solution steps

\int cos (a x) d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = a x

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

Add a constant to the solution

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

\frac{d ^{2}}{d x ^{2}} (5 x cos (x^{2}))

\int (3 - 2 x)^{5} d x

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

- sin (2 (3)) 3

7 (2 z e^{z} + e^{z} z^{2})