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

The integral from 1 to 2 of 4^{5x} is (523776)/(5ln(2))

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

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

\frac{523776}{5 ln ( 2 )}

Solution steps

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

Simplify

4^{5 x} : 102 4^{x}

= \int_{1}^{2} 102 4^{x} d x

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

= [\frac{102 4 ^{x}}{ln ( 1024 )}]_{1}^{2}

\frac{102 4 ^{x}}{ln ( 1024 )} = \frac{2 ^{10 x - 1}}{5 ln ( 2 )}

= [\frac{2 ^{10 x - 1}}{5 ln ( 2 )}]_{1}^{2}

Compute the boundaries:

\frac{523776}{5 ln ( 2 )}

= \frac{523776}{5 ln ( 2 )}

\int_{- 5}^{0} 2 (t + 1)^{\frac{1}{3}} d t

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

\int_{0}^{2} x e^{5 x} d x

\int_{- 10}^{10} (∣ x ∣ + 5) d x

What is the integral from 1 to 2 of 4^{5x} ?
The integral from 1 to 2 of 4^{5x} is (523776)/(5ln(2))