What is the integral of (cos(8sqrt(x)))/(sqrt(x)) ?

The integral of (cos(8sqrt(x)))/(sqrt(x)) is 1/4 sin(8sqrt(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(8sqrt(x)))/(sqrt(x))

\int \frac{cos ( 8 x )}{x} d x

\frac{1}{4} sin (8 x) + C

Solution steps

\int \frac{cos ( 8 x )}{x} d x

Apply u-substitution

: \int \frac{cos ( u )}{4} d u

= \int \frac{cos ( u )}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{4} sin (u)

Substitute back

u = 8 x

= \frac{1}{4} sin (8 x)

Add a constant to the solution

= \frac{1}{4} sin (8 x) + C

\int e^{9 x} sin (e^{9 x}) d x

\int 12 cos (4 θ) d θ

\int e^{6 x} sin (e^{6 x}) d x

\int sec^{2} (4 x) tan^{2} (4 x) d x

What is the integral of (cos(8sqrt(x)))/(sqrt(x)) ?
The integral of (cos(8sqrt(x)))/(sqrt(x)) is 1/4 sin(8sqrt(x))+C