What is the integral of 3*2^x ?

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

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integral of 3*2^x

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

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

Solution steps

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

Take the constant out:

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

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

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

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