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Popular >

integral of (3^{2x+1})

Solution

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

Solution

\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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\int x 8 x - x^{2} d x

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\int \frac{1}{6 x 1 - 36 x ^{2}} d x

Frequently Asked Questions (FAQ)

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