Question

Evaluate the following indefinite integrals.

Can you show all the steps please!

a) ∫xe^x^2+10 dx
b) ∫x-2/x-4 dx

Answer 1

∫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:
∫x-2/x-4 dx

using one step of a long division, we can show that
(x-2)/(x-4)
= 1 + 2/(x-4)

so ∫x-2/x-4 dx
= ∫1 + 2/x-4 dx
= x + 2ln(x-4) + C