en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 5^xe^x

Solution

\int 5^{x} e^{x} d x

Solution

\frac{( 5 e ) ^{x}}{ln ( 5 e )} + C

Solution steps

\int 5^{x} e^{x} d x

Apply exponent rule:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

5^{x} e^{x} = (5 e)^{x}

= \int (5 e)^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{( 5 e ) ^{x}}{ln ( 5 e )}

Add a constant to the solution

= \frac{( 5 e ) ^{x}}{ln ( 5 e )} + C

Graph

Popular Examples

integral of (x+1)cos(2x)

integral of 1/(sqrt((a^2-x^2)^3))

integral of (sqrt(16-e^{2x)})/(e^x)

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

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

Frequently Asked Questions (FAQ)

What is the integral of 5^xe^x ?
The integral of 5^xe^x is ((5e)^x)/(ln(5e))+C