Evaluate.
int {2 x} / {x^4 + 1} dx
2007-04-13 07:46:20 · 5 answers · asked by bhicks 1 in Science & Mathematics ➔ Mathematics
let x^2 = t ,then 2xdx=dt =>int {dt/t^2+1} = inv tan t+c = invtanx^2 +c
2007-04-13 07:54:50 · answer #1 · answered by wapa 1 · 1⤊ 0⤋
int{2x}/{x^4+1}dx or int{2x}/{x^2*x^2+1}=?
set: x^2=t
dt/dx=2x or dt=2xdx
then,
int(2x)/(x^2*x^2)dx=integral{dt}/{t^2+1}
we know that: integral{dt}/{t^2+1}=arctan{t}+k
with : t=x^2
the answer is: arctan{x^2}+k
or k is a constant...
2007-04-13 15:29:58 · answer #2 · answered by Johnny 2 · 0⤊ 0⤋
If you let u = x², then du = 2x dx
So you really have:
â¡du / (u² + 1)
= arctan u + C
= arctan (x²) + C
2007-04-13 14:55:53 · answer #3 · answered by Kathleen K 7 · 0⤊ 0⤋
Let's let u = x². Then du = 2x dx.
So we get
⫠du/(u²+1) = arctan u = arctan(x²) + C.
2007-04-13 14:57:54 · answer #4 · answered by steiner1745 7 · 0⤊ 0⤋
Use the substitution u = x^4 + 1. You can take it from there, I'm sure.
2007-04-13 14:51:53 · answer #5 · answered by acafrao341 5 · 0⤊ 2⤋