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

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

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integral of 3^{5x-1}

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

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

Solution steps

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

3^{5 x - 1} = 3^{- 1} \cdot 3^{5 x}

= \int 3^{- 1} \cdot 3^{5 x} d x

Take the constant out:

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

= 3^{- 1} \cdot \int 3^{5 x} d x

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \frac{1}{3} \cdot \int 3^{5 x} d x

Simplify

3^{5 x} : 24 3^{x}

= \frac{1}{3} \cdot \int 24 3^{x} d x

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

= \frac{1}{3} \cdot \frac{24 3 ^{x}}{ln ( 243 )}

Simplify

\frac{1}{3} \cdot \frac{24 3 ^{x}}{ln ( 243 )} : \frac{3 ^{5 x - 1}}{5 ln ( 3 )}

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

Add a constant to the solution

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

\frac{3 d y}{d x} = y^{2}

\frac{d}{d x} (\frac{x}{8 x + 8})

x \to 9 lim (\frac{x + 8}{x + 9})

\int 2 - 2 x d x

\frac{d}{d x} (3 x^{2} + x)

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