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+3e^x)

Solution

\int (x + 3 e^{x}) d x

Solution

\frac{x ^{2}}{2} + 3 e^{x} + C

Solution steps

\int x + 3 e^{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 3 e^{x} d x

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

\int 3 e^{x} d x = 3 e^{x}

= \frac{x ^{2}}{2} + 3 e^{x}

Add a constant to the solution

= \frac{x ^{2}}{2} + 3 e^{x} + C

Graph

Popular Examples

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

integral of 7xsin(x^2)

integral of 0.5e^{-0.7x}

integral of 1/((4x^2+9))

integral of sin(x)-sin^2(x)

Frequently Asked Questions (FAQ)

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