en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2+3^x)

Solution

\int (2 + 3^{x}) d x

Solution

2 x + \frac{3 ^{x}}{ln ( 3 )} + C

Solution steps

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

\int 2 d x = 2 x

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

= 2 x + \frac{3 ^{x}}{ln ( 3 )}

Add a constant to the solution

= 2 x + \frac{3 ^{x}}{ln ( 3 )} + C

Popular Examples

integral of (x^2+33)/(x^2+36)

\int \frac{x ^{2} + 33}{x ^{2} + 36} d x

integral of (2x^2+5x-1)/(x^3+x^2-2x)

\int \frac{2 x ^{2} + 5 x - 1}{x ^{3} + x ^{2} - 2 x} d x

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

\int \frac{1}{( 3 + sin ^{2} ( x ) )} d x

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

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

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

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

Frequently Asked Questions (FAQ)

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