What is the integral of 3^{2x+1} ?

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

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integral of 3^{2x+1}

\int 3^{2 x + 1} d x

\frac{3 ^{1 + 2 x}}{2 ln ( 3 )} + C

Solution steps

\int 3^{2 x + 1} d x

Apply Integration By Parts

: 3^{2 x + 1} x - \int 2 ln (3) \cdot 3^{2 x + 1} x d x

= 3^{2 x + 1} x - \int 2 ln (3) \cdot 3^{2 x + 1} x d x

\int 2 ln (3) \cdot 3^{2 x + 1} x d x = 3^{1 + 2 x} x - \frac{3 ^{1 + 2 x}}{2 ln ( 3 )}

= 3^{2 x + 1} x - (3^{1 + 2 x} x - \frac{3 ^{1 + 2 x}}{2 ln ( 3 )})

Simplify

= \frac{3 ^{1 + 2 x}}{2 ln ( 3 )}

Add a constant to the solution

= \frac{3 ^{1 + 2 x}}{2 ln ( 3 )} + C

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