Last two intergrals and I'm done for today's homework.
1) 3e^x / sqrt(1-e^(2x))
2) (3-x) / (x^2+4)
Also I got one intergral down to 1/u du, and is 1/u the same as ln|u|??
1)
You can rewrite the integral as follows:
Now our substitution will become evident. Let . .
Substitution into the integral, we have:
The integral of this is . Substitute the u value back in, and you get:
2)
I would recommend rewriting the integrand and then break it up into 2 integrals.
.
The first integral will take on the form of , in particular, it will be .
The second integral requires a substitution: . . Substituting into the second integral, we have:
.
This integral wll be . Substitute u back in and you get .
Thus:
Hope this answers your question!!!
Yes, splitting it into two integrals is a good idea :I solved the first one, but the second still confused me a bit on how to approach it. Should I split into two separate integrals? And what should u be for those?
For the first one, you can try and for the second one, . Otherwise, I wrote them so that you can integrate directly if you "see" the derivatives which are involved.