What is the integral of (sqrt(x)-3)/(2xsqrt(x)) ?

The integral of (sqrt(x)-3)/(2xsqrt(x)) is -(sqrt(x)-3)/(sqrt(x))+1/2 ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sqrt(x)-3)/(2xsqrt(x))

\int \frac{x - 3}{2 x x} d x

- \frac{x - 3}{x} + \frac{1}{2} ln ∣ x ∣ + C

Solution steps

\int \frac{x - 3}{2 x x} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{x - 3}{x x} d x

Apply Integration By Parts

: - \frac{2 ( x - 3 )}{x} - \int - \frac{1}{x} d x

= \frac{1}{2} (- \frac{2 ( x - 3 )}{x} - \int - \frac{1}{x} d x)

\int - \frac{1}{x} d x = - ln ∣ x ∣

= \frac{1}{2} (- \frac{2 ( x - 3 )}{x} - (- ln ∣ x ∣))

Simplify

\frac{1}{2} (- \frac{2 ( x - 3 )}{x} - (- ln ∣ x ∣)) : - \frac{x - 3}{x} + \frac{1}{2} ln ∣ x ∣

= - \frac{x - 3}{x} + \frac{1}{2} ln ∣ x ∣

Add a constant to the solution

= - \frac{x - 3}{x} + \frac{1}{2} ln ∣ x ∣ + C

\int \frac{sec ( x )}{sin ( x ) + cos ( x )} d x

\int \frac{ln ( x )}{x ^{2}} d x

\int \frac{1}{2 s - s ^{2}} d s

\int \frac{1}{16 e ^{6 x} - 25} d x

\int (x + 4)^{- 2} d x

What is the integral of (sqrt(x)-3)/(2xsqrt(x)) ?
The integral of (sqrt(x)-3)/(2xsqrt(x)) is -(sqrt(x)-3)/(sqrt(x))+1/2 ln|x|+C