Question

integral e^x/sqrt(e^2x + 9)

Answer 1

\[\int\limits_{}^{}\frac{ e ^{x} }{ e ^{2x} +9}dx\]

Answer 2

looks like arctangent more or less right?

Answer 3

try \(u=e^x\)

Answer 4

an arc tangent? how do you know by looking?

Answer 5

cause it looks like
\[\frac{1}{x^2+1}\] except with a 9

Answer 6

so if you put \(u=e^x\) and \(du=e^xdx\) you get
\[\int \frac{du}{u^2+9}\] right away

Answer 7

Make sure you remember your rules of exponents:\[\Large\sf e^{2x}=(e^x)^2\]Otherwise that denominator can look a little confusing.

Answer 8

\[\LaTeX\] master

Answer 9

what happens after this though?

Answer 10

well he said to use a tan sub
except you might want some constant multiple with that tan sub since you have a 9 there instead of 1