What is the integral of 2^{3x+5} ?

The integral of 2^{3x+5} is (2^{3x+5})/(3ln(2))+C

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integral of 2^{3x+5}

\int 2^{3 x + 5} d x

\frac{2 ^{3 x + 5}}{3 ln ( 2 )} + C

Solution steps

\int 2^{3 x + 5} d x

2^{3 x + 5} = 2^{5} \cdot 2^{3 x}

= \int 2^{5} \cdot 2^{3 x} d x

Take the constant out:

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

= 2^{5} \cdot \int 2^{3 x} d x

Simplify

= 32 \cdot \int 2^{3 x} d x

Simplify

2^{3 x} : 8^{x}

= 32 \cdot \int 8^{x} d x

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

= 32 \cdot \frac{8 ^{x}}{ln ( 8 )}

Simplify

32 \cdot \frac{8 ^{x}}{ln ( 8 )} : \frac{2 ^{3 x + 5}}{3 ln ( 2 )}

= \frac{2 ^{3 x + 5}}{3 ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{3 x + 5}}{3 ln ( 2 )} + C

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What is the integral of 2^{3x+5} ?
The integral of 2^{3x+5} is (2^{3x+5})/(3ln(2))+C