Write a value of `int(a^x)/(3+a^x)\ dx`

Explanation

Solution:

Let `t=3+a^{x} \Rightarrow d t=a^{x} \log a`

Now,

`I=\int \frac{a^{x} d x}{3+a^{x}}`

=`\frac{1}{\log a} \int \frac{d t}{t}`

=`\frac{1}{\log \{a}} \log \{t}+\{c}` \ldots \ldots . where c is the constant of integration.

=`\frac{1}{\log a} \log (3+a^{x}\right)+c` \quad \ldots \ldots \ldots where` t=3+a^x`