What is the integral from 0 to 2 of 3^{5x} ?

The integral from 0 to 2 of 3^{5x} is (59048)/(5ln(3))

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integral from 0 to 2 of 3^{5x}

\int_{0}^{2} 3^{5 x} d x

\frac{59048}{5 ln ( 3 )}

Decimal

10749.56117 \dots

Solution steps

\int_{0}^{2} 3^{5 x} d x

Simplify

3^{5 x} : 24 3^{x}

= \int_{0}^{2} 24 3^{x} d x

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

= [\frac{24 3 ^{x}}{ln ( 243 )}]_{0}^{2}

Simplify

ln (243) : 5 ln (3)

= [\frac{24 3 ^{x}}{5 ln ( 3 )}]_{0}^{2}

Compute the boundaries:

\frac{59048}{5 ln ( 3 )}

= \frac{59048}{5 ln ( 3 )}

\int_{0}^{2} (5 - x^{2}) d x

\int_{0}^{3} x^{4} - 3 x^{2} + 4 x d x

\int_{0}^{1} e^{x^{2}} x d x

\int_{0}^{2} 2 x + 1 d x

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

What is the integral from 0 to 2 of 3^{5x} ?
The integral from 0 to 2 of 3^{5x} is (59048)/(5ln(3))