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

The integral from 2 to 5 of 5^{4x} is (625^5-390625)/(4ln(5))

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

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

\frac{62 5 ^{5} - 390625}{4 ln ( 5 )}

Decimal

1.48138 E 13

Solution steps

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

Simplify

5^{4 x} : 62 5^{x}

= \int_{2}^{5} 62 5^{x} d x

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

= [\frac{62 5 ^{x}}{ln ( 625 )}]_{2}^{5}

Simplify

ln (625) : 4 ln (5)

= [\frac{62 5 ^{x}}{4 ln ( 5 )}]_{2}^{5}

Compute the boundaries:

\frac{62 5 ^{5} - 390625}{4 ln ( 5 )}

= \frac{62 5 ^{5} - 390625}{4 ln ( 5 )}

What is the integral from 2 to 5 of 5^{4x} ?
The integral from 2 to 5 of 5^{4x} is (625^5-390625)/(4ln(5))