What is the integral of 2*3^x ?

The integral of 2*3^x is (2*3^x)/(ln(3))+C

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integral of 2*3^x

\int 2 \cdot 3^{x} d x

\frac{2 \cdot 3 ^{x}}{ln ( 3 )} + C

Solution steps

\int 2 \cdot 3^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int 3^{x} d x

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

= 2 \cdot \frac{3 ^{x}}{ln ( 3 )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 \cdot 3 ^{x}}{ln ( 3 )}

Add a constant to the solution

= \frac{2 \cdot 3 ^{x}}{ln ( 3 )} + C

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