What is the integral of (3^x)/(ln(3)) ?

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

integral of (3^x)/(ln(3))

\int \frac{3 ^{x}}{ln ( 3 )} d x

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

Solution steps

\int \frac{3 ^{x}}{ln ( 3 )} d x

Take the constant out:

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{cot ( x )}{x})

d er i v a t i v e \frac{3 + x f ( x )}{x}

\frac{d}{d x} (ln (1 - \frac{10}{x}))

d er i v a t i v e f (x) = 5 x + 1

d er i v a t i v e f (x) = \frac{( tan ( x ) - 1 )}{sec ( x )}

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