Posted by Paul on .
Evaluate the following indefinite integrals.
Can you show all the steps please!
a) ∫xe^x^2+10 dx
b) ∫x2/x4 dx

Math 
Reiny,
∫xe^x^2+10 dx
the first term fits the pattern perfectly for differentiating terms of the type e^(u)
notice if I differentiate e^(x^2) , I get
2x e^(x^2), I am given half of that, so
∫xe^x^2+10 dx
= (1/2) e^(x^2) + 10x + C
for the second:
∫x2/x4 dx
using one step of a long division, we can show that
(x2)/(x4)
= 1 + 2/(x4)
so ∫x2/x4 dx
= ∫1 + 2/x4 dx
= x + 2ln(x4) + C