What is the integral of 8^{3x+5} ?

The integral of 8^{3x+5} is (8^{3x+5})/(9ln(2))+C

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integral of 8^{3x+5}

\int 8^{3 x + 5} d x

\frac{8 ^{3 x + 5}}{9 ln ( 2 )} + C

Solution steps

\int 8^{3 x + 5} d x

Apply u-substitution

: \int 8^{u} \cdot \frac{1}{3} d u

= \int 8^{u} \cdot \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int 8^{u} d u

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

= \frac{1}{3} \cdot \frac{8 ^{u}}{ln ( 8 )}

Substitute back

u = 3 x + 5

= \frac{1}{3} \cdot \frac{8 ^{3 x + 5}}{ln ( 8 )}

Simplify

\frac{1}{3} \cdot \frac{8 ^{3 x + 5}}{ln ( 8 )} : \frac{8 ^{3 x + 5}}{9 ln ( 2 )}

= \frac{8 ^{3 x + 5}}{9 ln ( 2 )}

Add a constant to the solution

= \frac{8 ^{3 x + 5}}{9 ln ( 2 )} + C

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What is the integral of 8^{3x+5} ?
The integral of 8^{3x+5} is (8^{3x+5})/(9ln(2))+C