What is the integral of ((6+x^2)/x) ?

The integral of ((6+x^2)/x) is 6ln|x|+(x^2)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((6+x^2)/x)

\int (\frac{6 + x ^{2}}{x}) d x

6 ln ∣ x ∣ + \frac{x ^{2}}{2} + C

Solution steps

\int \frac{6 + x ^{2}}{x} d x

Expand

\frac{6 + x ^{2}}{x} : \frac{6}{x} + x

= \int \frac{6}{x} + x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{6}{x} d x + \int x d x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

\int x d x = \frac{x ^{2}}{2}

= 6 ln ∣ x ∣ + \frac{x ^{2}}{2}

Add a constant to the solution

= 6 ln ∣ x ∣ + \frac{x ^{2}}{2} + C

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

\int \frac{e 4 x + 2}{4 x + 2} d x

\int \frac{1}{1 - e ^{2 x}} d x

\int \frac{( 6 x - 6 )}{x ^{2} - 2 x + 5} d x

\int \frac{x I n ^{5} ( x ^{2} + 3 )}{x ^{2} + 3} d x

What is the integral of ((6+x^2)/x) ?
The integral of ((6+x^2)/x) is 6ln|x|+(x^2)/2+C