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Popular Calculus >

integral of 5^xln(5)

Solution

\int 5^{x} ln (5) d x

Solution

5^{x} + C

Solution steps

\int 5^{x} ln (5) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= ln (5) \cdot \int 5^{x} d x

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

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

Simplify

ln (5) \frac{5 ^{x}}{ln ( 5 )} : 5^{x}

= 5^{x}

Add a constant to the solution

= 5^{x} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 5^xln(5) ?
The integral of 5^xln(5) is 5^x+C