What is the integral of (5^x)/(6^x) ?

The integral of (5^x)/(6^x) is (5^x)/(ln(5/6)*6^x)+C

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integral of (5^x)/(6^x)

\int \frac{5 ^{x}}{6 ^{x}} d x

\frac{5 ^{x}}{ln ( \frac{5}{6} ) \cdot 6 ^{x}} + C

Solution steps

\int \frac{5 ^{x}}{6 ^{x}} d x

Apply exponent rule:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= \int (\frac{5}{6})^{x} d x

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

= \frac{( \frac{5}{6} ) ^{x}}{ln ( \frac{5}{6} )}

Simplify

\frac{( \frac{5}{6} ) ^{x}}{ln ( \frac{5}{6} )} : \frac{5 ^{x}}{ln ( \frac{5}{6} ) \cdot 6 ^{x}}

= \frac{5 ^{x}}{ln ( \frac{5}{6} ) \cdot 6 ^{x}}

Add a constant to the solution

= \frac{5 ^{x}}{ln ( \frac{5}{6} ) \cdot 6 ^{x}} + C

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What is the integral of (5^x)/(6^x) ?
The integral of (5^x)/(6^x) is (5^x)/(ln(5/6)*6^x)+C