What is the integral from-1 to 2 of 5^{3x} ?

The integral from-1 to 2 of 5^{3x} is (1953124)/(375ln(5))

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integral from-1 to 2 of 5^{3x}

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

\frac{1953124}{375 ln ( 5 )}

Decimal

3236.11779 \dots

Solution steps

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

Simplify

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

= \int_{- 1}^{2} 12 5^{x} d x

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

= [\frac{12 5 ^{x}}{ln ( 125 )}]_{- 1}^{2}

Simplify

ln (125) : 3 ln (5)

= [\frac{12 5 ^{x}}{3 ln ( 5 )}]_{- 1}^{2}

Compute the boundaries:

\frac{1953124}{375 ln ( 5 )}

= \frac{1953124}{375 ln ( 5 )}

What is the integral from-1 to 2 of 5^{3x} ?
The integral from-1 to 2 of 5^{3x} is (1953124)/(375ln(5))