What is the integral of (3^x)/(4^x) ?

The integral of (3^x)/(4^x) is (3^x)/(ln(3/4)*4^x)+C

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integral of (3^x)/(4^x)

\int \frac{3 ^{x}}{4 ^{x}} d x

\frac{3 ^{x}}{ln ( \frac{3}{4} ) \cdot 4 ^{x}} + C

Solution steps

\int \frac{3 ^{x}}{4 ^{x}} d x

Apply exponent rule:

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

= \int (\frac{3}{4})^{x} d x

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

= \frac{( \frac{3}{4} ) ^{x}}{ln ( \frac{3}{4} )}

Simplify

\frac{( \frac{3}{4} ) ^{x}}{ln ( \frac{3}{4} )} : \frac{3 ^{x}}{ln ( \frac{3}{4} ) \cdot 4 ^{x}}

= \frac{3 ^{x}}{ln ( \frac{3}{4} ) \cdot 4 ^{x}}

Add a constant to the solution

= \frac{3 ^{x}}{ln ( \frac{3}{4} ) \cdot 4 ^{x}} + C

\frac{1}{2} e^{- 4 t} - \frac{1}{2} e^{- 6 t}

x \to 0 - lim (sin (x))

x^{2} y^{^{''}} + 2 x y^{^{'}} - 30 y = 0, y (1) = - 5, y^{^{'}} (1) = - 6

y^{^{''}} + 3 y = x

\int t ln (t + 3) d t

What is the integral of (3^x)/(4^x) ?
The integral of (3^x)/(4^x) is (3^x)/(ln(3/4)*4^x)+C