Question

How do you find the indefinite integral of `int (e^(7x)) / (e^(14x) + 36) dx`?

Answer 1

Refer to explanation

Explanation:

Set `u=e^(7x)=>du=e^(7x)(7)dx=>du=7e^(7x)dx`

Hence the integral becomes

#int (e^(7x))/(e^(14x)+36)dx= 1/7 int (du)/(u^2+36)= 1/7*1/6int 1/((u/6)^2+1)du= 1/7*1/6*arctan(u/6)+c#

Because `u=e^7x` we have that

`int (e^(7x))/(e^(14x)+36)dx=1/(7*6) arctan(e^(7x)/6)+c`