What is the integral from 0 to log_{3 of (5)}3^x ?

The integral from 0 to log_{3 of (5)}3^x is 4/(ln(3))

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integral from 0 to log_{3 of (5)}3^x

\int_{0}^{l o g_{3} (5)} 3^{x} d x

\frac{4}{ln ( 3 )}

Decimal Notation

3.64095 \dots

Solution steps

\int_{0}^{l o g_{3} (5)} 3^{x} d x

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

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

Compute the boundaries:

\frac{4}{ln ( 3 )}

= \frac{4}{ln ( 3 )}

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\int_{0}^{2} (5 x^{2} - 8 x + 4) d x

\int_{- 1}^{1} x^{2} - 2 x d x

\int_{0}^{2 π} 2 cos^{2} (t) d t

What is the integral from 0 to log_{3 of (5)}3^x ?
The integral from 0 to log_{3 of (5)}3^x is 4/(ln(3))