reduction formula (1 Viewer)

[bleakarcher]

I(n)=integral[1/(x^2+1)^n] dx
find I(n) in terms of I(n-1)

 

[Shadowdude]

Use integration by parts.

 

[muzeikchun852]

Use integration by parts.

tried that. doesn't really work.

edit: it does.

 

[Hermes1]

Use integration by parts.

what!!!!!!!!!!!!!!!!!!!! u use integration by parts for reduction formula, shock horror

 

[Shadowdude]

Reduction formulae work via integration by parts - so.. I don't know. I may have a try at it, but I'm sure other maths geniuses will be able to spot the correct way sooner than I =P

 

[muzeikchun852]

Reduction formulae work via integration by parts - so.. I don't know. I may have a try at it, but I'm sure other maths geniuses will be able to spot the correct way sooner than I =P

I think it's u=the whole thing / v'=1

 

[Hermes1]

im pretty sure i have seen a question like this before and it usually comes with a preceding step that allows us to solve the question. OP is trolling us again.

 

[Shadowdude]

Sorry for the double post but... are you sure that integral is correct?



?

 

[deterministic]

I think it's u=the whole thing / v'=1

This:

Should be easy from here, just replace n with n-1

 

[bleakarcher]

deterministic
i got to that point but i dont know where to go after it. i could do it if it was in term of I(n+1), i would be able to do it

 

[deterministic]

You have:

Just make the subject and replace n with n-1 in your final equation

 

[bleakarcher]

ahh ok. i wasnt familiar wif that. thanks man