What is the integral of 8^{3x+1} ?

The integral of 8^{3x+1} is (2^{9x+3})/(9ln(2))+C

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integral of 8^{3x+1}

\int 8^{3 x + 1} d x

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

Solution steps

\int 8^{3 x + 1} d x

Simplify

8^{3 x + 1} : 8^{3 x} \cdot 8

= \int 8^{3 x} \cdot 8 d x

Take the constant out:

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

= 8 \cdot \int 8^{3 x} d x

Simplify

8^{3 x} : 51 2^{x}

= 8 \cdot \int 51 2^{x} d x

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

= 8 \cdot \frac{51 2 ^{x}}{ln ( 512 )}

Simplify

8 \cdot \frac{51 2 ^{x}}{ln ( 512 )} : \frac{2 ^{9 x + 3}}{9 ln ( 2 )}

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 25})

\int \frac{( 1 + y ^{2} )}{y} d y

x^{2} + a x + b

\frac{d}{d x} (4 cos (π x))

\frac{693 x ^{\frac{5}{2}}}{8}

What is the integral of 8^{3x+1} ?
The integral of 8^{3x+1} is (2^{9x+3})/(9ln(2))+C