What is the integral of (2*3^x-5*2^x)/(3^x) ?

The integral of (2*3^x-5*2^x)/(3^x) is 2x-(5*2^x)/(ln(2/3)*3^x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (23^x-52^x)/(3^x)

\int \frac{2 \cdot 3 ^{x} - 5 \cdot 2 ^{x}}{3 ^{x}} d x

2 x - \frac{5 \cdot 2 ^{x}}{ln ( \frac{2}{3} ) \cdot 3 ^{x}} + C

Solution steps

\int \frac{2 \cdot 3 ^{x} - 5 \cdot 2 ^{x}}{3 ^{x}} d x

Expand

\frac{2 \cdot 3 ^{x} - 5 \cdot 2 ^{x}}{3 ^{x}} : 2 - \frac{5 \cdot 2 ^{x}}{3 ^{x}}

= \int 2 - \frac{5 \cdot 2 ^{x}}{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 2 d x - \int \frac{5 \cdot 2 ^{x}}{3 ^{x}} d x

\int 2 d x = 2 x

\int \frac{5 \cdot 2 ^{x}}{3 ^{x}} d x = \frac{5 \cdot 2 ^{x}}{ln ( \frac{2}{3} ) \cdot 3 ^{x}}

= 2 x - \frac{5 \cdot 2 ^{x}}{ln ( \frac{2}{3} ) \cdot 3 ^{x}}

Add a constant to the solution

= 2 x - \frac{5 \cdot 2 ^{x}}{ln ( \frac{2}{3} ) \cdot 3 ^{x}} + C

\int sin^{3} (5 x) cos (5 x) d x

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

\int \frac{x ^{2}}{1 - x ^{4}} d x

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

\int \frac{x ^{2} + 4 x + 27}{( x - 2 ) ( x ^{2} + 9 )} d x

What is the integral of (2*3^x-5*2^x)/(3^x) ?
The integral of (2*3^x-5*2^x)/(3^x) is 2x-(5*2^x)/(ln(2/3)*3^x)+C