I'm having trouble solving:

even though I have the answer. It is getting from step to step that is hard.

Step 2 is:

Step 3 is:

I can't really figure out where they got their antiderivatives, which is what I thought was supposed to go right before the vertical bar in the step right after the one that includes the integration symbol. The coefficients on what I'm supposed to integrate were 2/3 and the coefficients on (what I think are) the anti-derivatives are -2. (I thought the antiderivative of e to a power was e to that power.)

I think that going from step 2 to step 3 means that:

but I can't figure out why that is the case. Is

really the antiderivative of

? Or is something else going on there?

The solution to the problem (step 4) is

. Getting from step 3 to that is easy.