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

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

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integral of 3^{-2x+1}

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{1}{2} \cdot 3^{u} d u

= \int - \frac{1}{2} \cdot 3^{u} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int 3^{u} d u

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

= - \frac{1}{2} \cdot \frac{3 ^{u}}{ln ( 3 )}

Substitute back

u = - 2 x + 1

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

Simplify

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

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

Add a constant to the solution

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

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