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

The integral from 0 to 1 of 3^{2x} is 4/(ln(3))

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

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

\frac{4}{ln ( 3 )}

Decimal Notation

3.64095 \dots

Solution steps

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

Simplify

3^{2 x} : 9^{x}

= \int_{0}^{1} 9^{x} d x

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

= [\frac{9 ^{x}}{ln ( 9 )}]_{0}^{1}

Simplify

ln (9) : 2 ln (3)

= [\frac{9 ^{x}}{2 ln ( 3 )}]_{0}^{1}

Compute the boundaries:

\frac{4}{ln ( 3 )}

= \frac{4}{ln ( 3 )}

\int_{0}^{x^{3}} y e^{- \frac{y}{x}} d y

\int_{0}^{1} 11 \frac{1}{x ^{p}} d x

y = sin (tan (9 x))

f (x) = - 3 x^{3} + 4, at x = - 1

\frac{\partial}{\partial x} (m x^{b})

What is the integral from 0 to 1 of 3^{2x} ?
The integral from 0 to 1 of 3^{2x} is 4/(ln(3))