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

The integral from 0 to 2 of 5^{3x} is (5208)/(ln(5))

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

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

\frac{5208}{ln ( 5 )}

Solution steps

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

Simplify

5^{3 x} : 12 5^{x}

= \int_{0}^{2} 12 5^{x} d x

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

= [\frac{12 5 ^{x}}{ln ( 125 )}]_{0}^{2}

Simplify

ln (125) : 3 ln (5)

= [\frac{12 5 ^{x}}{3 ln ( 5 )}]_{0}^{2}

Compute the boundaries:

\frac{5208}{ln ( 5 )}

= \frac{5208}{ln ( 5 )}

\int_{0}^{2} (2 x^{3} - 2 x) d x

\int_{1}^{3} 2^{5 x} d x

\int_{0}^{3} \frac{2 x}{( x ^{2} + 3 ) ^{2}} d x

\int_{1}^{3} 9 d x

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

What is the integral from 0 to 2 of 5^{3x} ?
The integral from 0 to 2 of 5^{3x} is (5208)/(ln(5))