Question

find anti derivative of given eq by method of inspection.explain the steps.
1.) e^2x 2.) (ax+b)^2

Answer 1

make an educated guess ....

Answer 2

e^u derives to u' e^u

e^2x derives to 2 e^2x, which is close to what we want, so lets use a 2/2 to help out, since 1* anything changes nothing

e^2x = 2e^2x / 2 and
comes from e^2x /2

Answer 3

a ^2 comes from some ^3 so take make a guess:

(ax+b)^3 derives to 3a(ax+b)2

so lets multiply the setup by 3a/3a to create something useful