Question

integration of (2^x+3^x)/5^x

Answer 1

Solution :

Now, $\displaystyle \mathsf{\int \frac{2^{x}+3^{x}}{5^{x}}dx}$

$\displaystyle \mathsf{=\int \frac{2^{x}}{5^{x}}dx+\int \frac{3^{x}}{5^{x}}dx}$

$\displaystyle \mathsf{=\int (\frac{2}{5})^{x}dx+\int (\frac{3}{5})^{x}dx}$

$\displaystyle \mathsf{=\frac{(\frac{2}{5})^{x}}{log_{e}\frac{2}{5}}+\frac{(\frac{3}{5})^{x}}{log_{e}\frac{3}{5}}+C}$

where C is constant of integration.

Rule :

1. $\displaystyle \mathsf{\frac{a^{c}}{b^{c}}=(\frac{a}{b})^{c}}$

2. $\displaystyle \mathsf{\int a^{x}\:dx=\frac{a^{x}}{log_{e}a}+C}$

where C is constant of integration

Answer 2

Step-by-step explanation:

$\huge\underline\mathfrak\purple{Solution}$