What is the integral from 0 to 1 of ln(7)7^x ?

The integral from 0 to 1 of ln(7)7^x is 6

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integral from 0 to 1 of ln(7)7^x

\int_{0}^{1} ln (7) 7^{x} d x

6

Solution steps

\int_{0}^{1} ln (7) \cdot 7^{x} d x

Take the constant out:

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

= ln (7) \cdot \int_{0}^{1} 7^{x} d x

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

= ln (7) [\frac{7 ^{x}}{ln ( 7 )}]_{0}^{1}

Compute the boundaries:

\frac{6}{ln ( 7 )}

= ln (7) \frac{6}{ln ( 7 )}

Simplify

= 6

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What is the integral from 0 to 1 of ln(7)7^x ?
The integral from 0 to 1 of ln(7)7^x is 6