What is the integral from 0 to 1/2 of 5^{2x} ?

The integral from 0 to 1/2 of 5^{2x} is 2/(ln(5))

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integral from 0 to 1/2 of 5^{2x}

\int_{0}^{\frac{1}{2}} 5^{2 x} d x

\frac{2}{ln ( 5 )}

Decimal

1.24266 \dots

Solution steps

\int_{0}^{\frac{1}{2}} 5^{2 x} d x

Simplify

5^{2 x} : 2 5^{x}

= \int_{0}^{\frac{1}{2}} 2 5^{x} d x

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

= [\frac{2 5 ^{x}}{ln ( 25 )}]_{0}^{\frac{1}{2}}

Simplify

ln (25) : 2 ln (5)

= [\frac{2 5 ^{x}}{2 ln ( 5 )}]_{0}^{\frac{1}{2}}

Compute the boundaries:

\frac{2}{ln ( 5 )}

= \frac{2}{ln ( 5 )}

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What is the integral from 0 to 1/2 of 5^{2x} ?
The integral from 0 to 1/2 of 5^{2x} is 2/(ln(5))