What is the integral of 1/(sqrt(ax)) ?

The integral of 1/(sqrt(ax)) is (2sqrt(x))/(sqrt(a))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(sqrt(ax))

\int \frac{1}{a x} d x

\frac{2 x}{a} + C

Solution steps

\int \frac{1}{a x} d x

\frac{1}{a x} = \frac{1}{a} \frac{1}{x}

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

Take the constant out:

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

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

Apply the Power Rule

: 2 x^{\frac{1}{2}}

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

Simplify

\frac{1}{a} \cdot 2 x^{\frac{1}{2}} : \frac{2 x}{a}

= \frac{2 x}{a}

Add a constant to the solution

= \frac{2 x}{a} + C

\int \frac{4}{( 4 x - 3 ) ln ( 4 x - 3 )} d x

\int 5 x^{3} ln (x) d x

\int x (1 + x^{2})^{\frac{5}{2}} d x

\int \frac{x + 3}{x ^{2} - 16} d x

\int 24 csc (4 x) sec (4 x) d x

What is the integral of 1/(sqrt(ax)) ?
The integral of 1/(sqrt(ax)) is (2sqrt(x))/(sqrt(a))+C