en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 2x^2+3/x

Solution

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

Solution

\frac{2 x ^{3}}{3} + 3 ln ∣ x ∣ + C

Solution steps

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

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{2 x ^{3}}{3} + 3 ln ∣ x ∣

Add a constant to the solution

= \frac{2 x ^{3}}{3} + 3 ln ∣ x ∣ + C

Graph

Popular Examples

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

integral of \sqrt[4]{16}cos(x)

integral of cos(x)-4

integral of sqrt(x^{15)}

integral of (x^2)/(sqrt(x^2+2x-3))

Frequently Asked Questions (FAQ)

What is the integral of 2x^2+3/x ?
The integral of 2x^2+3/x is (2x^3)/3+3ln|x|+C