What is the integral of (sqrt(inx))/x ?

The integral of (sqrt(inx))/x is 2sqrt(x)sqrt(in)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (sqrt(inx))/x

\int \frac{in x}{x} d x

2 x in + C

Solution steps

\int \frac{in x}{x} d x

\frac{in x}{x} = in \frac{x}{x}

= \int in \frac{x}{x} d x

Take the constant out:

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

= in \cdot \int \frac{x}{x} d x

Simplify

\frac{x}{x} : \frac{1}{x}

= in \cdot \int \frac{1}{x} d x

Apply the Power Rule

= in \cdot 2 x^{\frac{1}{2}}

Apply radical rule:

= 2 x in

Add a constant to the solution

= 2 x in + C

What is the integral of (sqrt(inx))/x ?
The integral of (sqrt(inx))/x is 2sqrt(x)sqrt(in)+C