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

The integral of (a^x)/(b^x) is (a^x)/(b^xln(a/b))+C

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

\int \frac{a ^{x}}{b ^{x}} d x

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

Solution steps

\int \frac{a ^{x}}{b ^{x}} d x

Simplify

\frac{a ^{x}}{b ^{x}} : (\frac{a}{b})^{x}

= \int (\frac{a}{b})^{x} d x

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

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

Simplify

\frac{( \frac{a}{b} ) ^{x}}{ln ( \frac{a}{b} )} : \frac{a ^{x}}{b ^{x} ln ( \frac{a}{b} )}

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

Add a constant to the solution

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

\frac{- x ^{2} - 9}{( x ^{2} - 9 ) ^{2}}

y^{2} = 2 x - 2, y = x - 5

\frac{\partial}{\partial x} (cos (x^{2} y))

\int - 2 x + 18 x^{2} - 4 x^{3} + 18 d x

What is the integral of (a^x)/(b^x) ?
The integral of (a^x)/(b^x) is (a^x)/(b^xln(a/b))+C