Question

Does integral of x^2/(x^2+1)= 1/3*x^3*tanx+c?

Answer 1

nopes.

Answer 2

I would do this with long division first, then integrate

Answer 3

you could just do the trig sub though

Answer 4

But why doesn't it equal to right hand side?

Answer 5

or u can write numerator as
x^2 + 1 - 1
and then separate the denominator.

Answer 6

I dunno, I would have to do the integral, and I'm a bit distracted. It's a troll fest today

Answer 7

@hartnn that's what I would do as well

Answer 8

yup, that would simply lead to
1- 1/ (1+x^2)

Answer 9

which can be integrated by standard formulas.

Answer 10

So there's no way I can integrate x^2 and 1/(x^2+1) separately?

Answer 11

no, the given function is product of these two functions...and integration does not distribute on product.

Answer 12

Alright, thanks. :)

Answer 13

welcome :)

Answer 14

heres another way
add ans subtract 1 in numerator
x^2+1-1 /(x^2+1)

now rewrite this

(x^2+1)/( x^2+1) - 1/(x^2+1)

Answer 15

which works out to 1- 1/(x^2+1)

Answer 16

and you already have answer for intergral of x^2+1

Answer 17

i mean 1/ (x^2+1)

Answer 18

@psi9epsilon please read those who have answered before you, @hartnn gave that exact method already

Answer 19

@turing test, sure but with incomplete explanation

Answer 20

@TuringTest , atleast show some work to make them understand

Answer 21

I thought it was sufficient, but oh well...

Answer 22

@TuringTest , i agree with you too, no dispute : )