post 34

well dang, i forgot to do my blog last weekend, stupid spring break... well anyways. on to this blog...

substitution:
Substitution takes the place of the derivative rules for problems with a quotient rule and product rule, substitution has a few steps.

1. find u by looking inside the parentheses inside the problem
2. take the derivative of u to find du
3. go into the origional problem and switch out (substitute) the stuff
4. integrate
5. plug in

ok, so ln i kinda understand, ln integration happens when the bottom of a fraction is the u and the top is the derivative of u. so since the derivative of ln(x) is 1/x, the answer is just ln(u)+c like everytime.

e^x integration is pretty decent too, all you have to do for this kind of integration is set your u equal to the exponent of the e. So the derivative of e^x is just e^x times the derivative of x.