What is the integral from-infinity to 0 of 3^x ?

The integral from-infinity to 0 of 3^x is 1/(ln(3))

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integral from-infinity to 0 of 3^x

\int_{- \infty}^{0} 3^{x} d x

\frac{1}{ln ( 3 )}

Decimal Notation

0.91023 \dots

Solution steps

\int_{- \infty}^{0} 3^{x} d x

Compute the indefinite integral:

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )} + C

Compute the boundaries:

\int_{- \infty}^{0} 3^{x} d x = \frac{1}{ln ( 3 )} - 0

= \frac{1}{ln ( 3 )} - 0

Simplify

= \frac{1}{ln ( 3 )}

6 y^{^{''}} + 23 y^{^{'}} - 4 y = 0

\frac{d}{d x} ((x - 4) (\frac{x}{2} + 1)^{3})

\frac{\partial}{\partial x} (7 e^{x y + 8})

\frac{d}{d x} ((x + 1)^{3} (x - 1)^{2})

\int e^{7 x - 5} d x

What is the integral from-infinity to 0 of 3^x ?
The integral from-infinity to 0 of 3^x is 1/(ln(3))