What is the integral of (3^x)/(e^x) ?

The integral of (3^x)/(e^x) is (3^x)/((ln(3)-1)e^x)+C

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integral of (3^x)/(e^x)

\int \frac{3 ^{x}}{e ^{x}} d x

\frac{3 ^{x}}{( ln ( 3 ) - 1 ) e ^{x}} + C

Solution steps

\int \frac{3 ^{x}}{e ^{x}} d x

Apply exponent rule:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= \int (\frac{3}{e})^{x} d x

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

= \frac{( \frac{3}{e} ) ^{x}}{ln ( \frac{3}{e} )}

Simplify

\frac{( \frac{3}{e} ) ^{x}}{ln ( \frac{3}{e} )} : \frac{3 ^{x}}{( ln ( 3 ) - 1 ) e ^{x}}

= \frac{3 ^{x}}{( ln ( 3 ) - 1 ) e ^{x}}

Add a constant to the solution

= \frac{3 ^{x}}{( ln ( 3 ) - 1 ) e ^{x}} + C

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What is the integral of (3^x)/(e^x) ?
The integral of (3^x)/(e^x) is (3^x)/((ln(3)-1)e^x)+C