en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of x+ln(x)

Solution

\int x + ln (x) d x

Solution

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

Solution steps

\int x + 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 ln (x) d x

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

limit as x approaches 0+of-x+1

x \to 0 + lim (- x + 1)

y^'= y/x+(y/x)^2

y^{^{'}} = \frac{y}{x} + (\frac{y}{x})^{2}

derivative of \sqrt[3]{t}

d er i v a t i v e 3 t

integral of sqrt(x)-(x-2)

\int x - (x - 2) d x

derivative of ln(w)

d er i v a t i v e ln (w)

Frequently Asked Questions (FAQ)

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