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

The integral from 2 to 3 of 3^{5x} is (14289858)/(5ln(3))

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

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

\frac{14289858}{5 ln ( 3 )}

Decimal Notation

2601437.85890 \dots

Solution steps

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

Simplify

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

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

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

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

Simplify

ln (243) : 5 ln (3)

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

Compute the boundaries:

\frac{14289858}{5 ln ( 3 )}

= \frac{14289858}{5 ln ( 3 )}

\int_{2}^{3} - t^{2} + 2 t + 3 d t

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

\int_{0}^{π} π cos (n x) d x

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

\int_{0}^{\frac{π}{3}} 2 cos (x) d x

What is the integral from 2 to 3 of 3^{5x} ?
The integral from 2 to 3 of 3^{5x} is (14289858)/(5ln(3))