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

The integral from 1 to 4 of 2^{5x} is (1048544)/(5ln(2))

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

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

\frac{1048544}{5 ln ( 2 )}

Decimal

302545.84579 \dots

Solution steps

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

Simplify

2^{5 x} : 3 2^{x}

= \int_{1}^{4} 3 2^{x} d x

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

= [\frac{3 2 ^{x}}{ln ( 32 )}]_{1}^{4}

Simplify

ln (32) : 5 ln (2)

= [\frac{3 2 ^{x}}{5 ln ( 2 )}]_{1}^{4}

Compute the boundaries:

\frac{1048544}{5 ln ( 2 )}

= \frac{1048544}{5 ln ( 2 )}

\int_{0}^{\infty} x^{4} d x

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

\int_{1}^{6} (\frac{5}{x}) d x

\int_{1}^{3} x^{2} y d y

\int_{0}^{1} 5 - x^{3} d x

What is the integral from 1 to 4 of 2^{5x} ?
The integral from 1 to 4 of 2^{5x} is (1048544)/(5ln(2))