en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x+2ln(x)

Solution

\int x + 2 ln (x) d x

Solution

\frac{x ^{2}}{2} + 2 (x ln (x) - x) + C

Solution steps

\int x + 2 ln (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 x d x + \int 2 ln (x) d x

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

\int 2 ln (x) d x = 2 (x ln (x) - x)

= \frac{x ^{2}}{2} + 2 (x ln (x) - x)

Add a constant to the solution

= \frac{x ^{2}}{2} + 2 (x ln (x) - x) + C

Graph

Popular Examples

integral of y*e^{xy}

\int y \cdot e^{x y} d x

integral of (3x)/(2x+1)

\int \frac{3 x}{2 x + 1} d x

integral of 8x^2e^{2x}

\int 8 x^{2} e^{2 x} d x

integral of 1/(sqrt(x+2)+3)

\int \frac{1}{x + 2 + 3} d x

integral of 2x(4x^2-3)^3

\int 2 x (4 x^{2} - 3)^{3} d x

Frequently Asked Questions (FAQ)

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