What is the integral of 5^{3x+1} ?

The integral of 5^{3x+1} is (5^{3x+1})/(3ln(5))+C

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integral of 5^{3x+1}

\int 5^{3 x + 1} d x

\frac{5 ^{3 x + 1}}{3 ln ( 5 )} + C

Solution steps

\int 5^{3 x + 1} d x

Simplify

5^{3 x + 1} : 5^{3 x} \cdot 5

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

Take the constant out:

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

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

Simplify

5^{3 x} : 12 5^{x}

= 5 \cdot \int 12 5^{x} d x

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

= 5 \cdot \frac{12 5 ^{x}}{ln ( 125 )}

Simplify

5 \cdot \frac{12 5 ^{x}}{ln ( 125 )} : \frac{5 ^{3 x + 1}}{3 ln ( 5 )}

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

Add a constant to the solution

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

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What is the integral of 5^{3x+1} ?
The integral of 5^{3x+1} is (5^{3x+1})/(3ln(5))+C