What is the integral of (cos(7sqrt(x)))/(sqrt(x)) ?

The integral of (cos(7sqrt(x)))/(sqrt(x)) is 2/7 sin(7sqrt(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (cos(7sqrt(x)))/(sqrt(x))

\int \frac{cos ( 7 x )}{x} d x

\frac{2}{7} sin (7 x) + C

Solution steps

\int \frac{cos ( 7 x )}{x} d x

Apply u-substitution

= \int \frac{2 cos ( u )}{7} d u

Take the constant out:

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

= \frac{2}{7} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{2}{7} sin (u)

Substitute back

u = 7 x

= \frac{2}{7} sin (7 x)

Add a constant to the solution

= \frac{2}{7} sin (7 x) + C

What is the integral of (cos(7sqrt(x)))/(sqrt(x)) ?
The integral of (cos(7sqrt(x)))/(sqrt(x)) is 2/7 sin(7sqrt(x))+C