What is the integral of (3^x)/(2^x) ?

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

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integral of (3^x)/(2^x)

\int \frac{3 ^{x}}{2 ^{x}} d x

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

Solution steps

\int \frac{3 ^{x}}{2 ^{x}} d x

Apply exponent rule:

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

= \int (\frac{3}{2})^{x} d x

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

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

Simplify

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

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

Add a constant to the solution

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

x \to 0 lim (15)

\int \frac{6 x}{x ^{2} + 4} d x

(- 2, 7), (0, 5)

\frac{d}{d v} (\frac{u}{v})

x \to 0 lim ((1 + 7 x)^{\frac{5}{x}})

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