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

The integral of 8^{5x+5} is (32768^{x+1})/(15ln(2))+C

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integral of 8^{5x+5}

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

\frac{3276 8 ^{x + 1}}{15 ln ( 2 )} + C

Solution steps

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

8^{5 x + 5} = 8^{5} \cdot 8^{5 x}

= \int 8^{5} \cdot 8^{5 x} d x

Take the constant out:

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

= 8^{5} \cdot \int 8^{5 x} d x

Simplify

= 32768 \cdot \int 8^{5 x} d x

Simplify

8^{5 x} : 3276 8^{x}

= 32768 \cdot \int 3276 8^{x} d x

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

= 32768 \cdot \frac{3276 8 ^{x}}{ln ( 32768 )}

Simplify

32768 \cdot \frac{3276 8 ^{x}}{ln ( 32768 )} : \frac{3276 8 ^{x + 1}}{15 ln ( 2 )}

= \frac{3276 8 ^{x + 1}}{15 ln ( 2 )}

Add a constant to the solution

= \frac{3276 8 ^{x + 1}}{15 ln ( 2 )} + C

What is the integral of 8^{5x+5} ?
The integral of 8^{5x+5} is (32768^{x+1})/(15ln(2))+C