What is the integral from 0 to 3 of 5^xln(5) ?

The integral from 0 to 3 of 5^xln(5) is 124

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integral from 0 to 3 of 5^xln(5)

\int_{0}^{3} 5^{x} ln (5) d x

124

Solution steps

\int_{0}^{3} 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_{0}^{3} 5^{x} d x

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

= ln (5) [\frac{5 ^{x}}{ln ( 5 )}]_{0}^{3}

Compute the boundaries:

\frac{124}{ln ( 5 )}

= ln (5) \frac{124}{ln ( 5 )}

Simplify

= 124

What is the integral from 0 to 3 of 5^xln(5) ?
The integral from 0 to 3 of 5^xln(5) is 124