What is the integral from 1 to 4 of 5^{2x} ?

The integral from 1 to 4 of 5^{2x} is (195300)/(ln(5))

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integral from 1 to 4 of 5^{2x}

\int_{1}^{4} 5^{2 x} d x

\frac{195300}{ln ( 5 )}

Decimal Notation

121346.71271 \dots

Solution steps

\int_{1}^{4} 5^{2 x} d x

Simplify

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

= \int_{1}^{4} 2 5^{x} d x

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

= [\frac{2 5 ^{x}}{ln ( 25 )}]_{1}^{4}

Simplify

ln (25) : 2 ln (5)

= [\frac{2 5 ^{x}}{2 ln ( 5 )}]_{1}^{4}

Compute the boundaries:

\frac{195300}{ln ( 5 )}

= \frac{195300}{ln ( 5 )}

\int_{0}^{\frac{1}{2}} (2 x) d x

\int_{- 1}^{2} 9 - x^{2} d x

\int_{1}^{10} \frac{20}{x} d x

\int_{- 2}^{3} 9 - x^{2} d x

\int_{e^{1}}^{e^{2}} \frac{1}{x ln ( x )} d x

What is the integral from 1 to 4 of 5^{2x} ?
The integral from 1 to 4 of 5^{2x} is (195300)/(ln(5))