Question

integration of (x^2-1)/(x^2+1)(x^4+1)^1/2 HELP!!

Answer 1

\[\int\limits_{}^{}\frac{ x ^{2}-1 }{ (x ^{2}+1)\sqrt{x ^{4}+1} }dx\]

correct?

Answer 2

Yes

Answer 3

There is hint given ... Decide numerator and denominator by x^2 and then substitute x+1/x =t

Answer 4

Devide *

Answer 5

But I'm not getting the equation after I dividing

Answer 6

Trying to make sense of the substitution, sorry.

Answer 7

No it's k ... Maybe ill show u the options

Answer 8

Finally the option got uploaded sorry

Answer 9

@Psymon help her lol

Answer 10

Haha he tried :)

Answer 11

yeah, I got too stuck on looking at your substitution. Seeing the answer options I know what to do now, though x_x

Answer 12

we'll follow the hint (divide both sides by x^2
\[\Large \frac{x^2-1}{(x^2+1)\sqrt{x^4+1}}\cdot\frac{\tfrac{1}{x^2}}{\tfrac{1}{x^2}}\]
split \[\frac{1}{x^2}\] into the two factors in the denominator as \[(x^2+1)\frac{1}{x}\cdot\sqrt{x^4+1}\cdot\sqrt{\frac{1}{x^2}}\]

Answer 13

Oh yes then you can substitute ...

Answer 14

the resulting integral is \[\Large \frac{(1-\frac{1}{x^2})}{(x+\frac{1}{x})\sqrt{x^2+\frac{1}{x^2}}}\]
let \[t=x+1/x\] as suggested
\[dt=(1-1/x^2) dx\]

Answer 15

Let me try

Answer 16

Ah, I misunderstood the substitution. I thought x+1 was the whole numerator.

Answer 17

Thanx....

Answer 18

YW

Answer 19

Shouldve made sure that was the correct interpretation x_x

Answer 20

Haha don't worry u don't know what all ive kept substituting .. :p

Answer 21

My method is trig substiution for this. But not sure if you've seen that or not.

Answer 22

I've seen for other sums trig substitution ... This one I m not sure ...

Answer 23

You'd have to say that x^2 = tan(theta) and thw whole (x^4+1)^(1/2) = sec(theta).

Answer 24

Yes yes that's another way .... But there is more to this question then just substituting ... I've got the answer thank u ... :)