Question

Find the indefinite integral of ((e^x+e^2x)^2)/e^3xdx

Answer 1

Step 1 here for sure is to expand out that term in brackets and then simplify everything so you just get a sum of exponential functions

Answer 2

...the idea being that you know how to integrate e^(ax) for any value of a, right?

Answer 3

Isn't it the integral just the same? I know that the integral of e^x is just e^x but is it different with e^ax?

Answer 4

what's the derivative of \( e^{ax} \)? It is \( a e^{ax} \).

Hence

\[ \int e^{ax} \ dx = \frac{1}{a} e^{ax} + C \]

Answer 5

Thank you :)