What is the integral from 0 to 1 of 2^{3x} ?

The integral from 0 to 1 of 2^{3x} is 7/(3ln(2))

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integral from 0 to 1 of 2^{3x}

\int_{0}^{1} 2^{3 x} d x

\frac{7}{3 ln ( 2 )}

Decimal

3.36628 \dots

Solution steps

\int_{0}^{1} 2^{3 x} d x

Simplify

2^{3 x} : 8^{x}

= \int_{0}^{1} 8^{x} d x

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

= [\frac{8 ^{x}}{ln ( 8 )}]_{0}^{1}

Simplify

ln (8) : 3 ln (2)

= [\frac{8 ^{x}}{3 ln ( 2 )}]_{0}^{1}

Compute the boundaries:

\frac{7}{3 ln ( 2 )}

= \frac{7}{3 ln ( 2 )}

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\int_{- 1}^{1} \frac{12}{1 + x ^{2}} d x

\int_{0}^{π} \frac{7}{3} sin (x) d x

What is the integral from 0 to 1 of 2^{3x} ?
The integral from 0 to 1 of 2^{3x} is 7/(3ln(2))