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

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

Popular >

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

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

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

Solution steps

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

Expand

\frac{3 ^{x} + 2 ^{x}}{3 ^{x}} : 1 + (\frac{2}{3})^{x}

= \int 1 + (\frac{2}{3})^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int (\frac{2}{3})^{x} d x

\int 1 d x = x

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

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

Add a constant to the solution

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

\int \frac{x}{x + 9} d x

\int \frac{2 - x}{9 - 4 x ^{2}} d x

\int \frac{x - 3}{( x + 1 ) ( x ^{2} + 9 )} d x

\int \frac{x ^{2} - 1}{x ^{3} - 3 x + 2} d x

\int (\frac{1}{t} - 1) \frac{1}{t ^{2}} d t

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