What is the integral from 1 to 2 of 3^{4x} ?

The integral from 1 to 2 of 3^{4x} is (1620)/(ln(3))

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integral from 1 to 2 of 3^{4x}

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

\frac{1620}{ln ( 3 )}

Decimal

1474.58754 \dots

Solution steps

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

Simplify

3^{4 x} : 8 1^{x}

= \int_{1}^{2} 8 1^{x} d x

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

= [\frac{8 1 ^{x}}{ln ( 81 )}]_{1}^{2}

Simplify

ln (81) : 4 ln (3)

= [\frac{8 1 ^{x}}{4 ln ( 3 )}]_{1}^{2}

Compute the boundaries:

\frac{1620}{ln ( 3 )}

= \frac{1620}{ln ( 3 )}

\int_{1}^{3} 6 x d x

\int_{- 1}^{2} \frac{1}{x + 2} d x

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

\int_{0}^{0.8} e^{- x^{2}} d x

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

What is the integral from 1 to 2 of 3^{4x} ?
The integral from 1 to 2 of 3^{4x} is (1620)/(ln(3))