Posted by **Paul** on Friday, March 15, 2013 at 1:08pm.

Evaluate the following indefinite integrals.

Can you show all the steps please!

a) ∫xe^x^2+10 dx

b) ∫x-2/x-4 dx

- Math -
**Reiny**, Friday, March 15, 2013 at 2:03pm
∫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

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