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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

f (x) = \frac{x}{x + 6}

\int (ln (x) + 1) e^{x l n (x)} d x

\int x^{- 2} e^{- \frac{1}{x}} d x

\frac{d}{d x} (ln (x x^{2} - 12))

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

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