Question

Got stuck on a integral, on which I can't seem to do partial fractions on.

Integrate: 1 / (x (x^2+1))
Wolfram didn't really help me at all :(.

Answer 1

Just go to show steps and it shows you what it does for partial fractions

Answer 2

I don't understand how it did that. :/,

For example it says u = x^2 and then the normal X becomes u?

Answer 3

yup u substitution...have you done that before?

Answer 4

Yes, I have but if you look at wolframs substition, u=x^2 but the normal x becomes u aswell.

Answer 5

do you see the part that says du= 2x dx
???

Answer 6

yes, does that allow x to become u?

Answer 7

well isolate dx
dx= (1/2x) du

Answer 8

replace dx with that now

Answer 9

and you already have a 1/x in there so 1/x * 1/x = 1/x^2

Answer 10

and u=x^2

Answer 11

so you get 1/u

Answer 12

but you also see the 1/2 right that's where it came from

Answer 13

HOLY pellet!, but the constant 1/2 goes outside the integral right?

Answer 14

yup the half is put out

Answer 15

wow thanks alot! understand it now!

Answer 16

then the next part is partial fractions and I'll have to review it if you need help on that too. it's been a while.

Answer 17

or w/e it called the integration by parts...

Answer 18

partial fractions: A/u + B/u+1

and then find out A and B right?

Answer 19

sounds about right....don't take my word for it

Answer 20

:) thanks alot! for helping understand it now!.