I'm trying to study for a Calc test tomorrow but i'm really having problem understanding one part of this problem. I already came up with the right aswer, but only b/c the multiple choice questions kinda gave it away, I really need help plz
Evaluate the integral:
integral [ x/(81+x^4)] dx
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Here is where the problem starts...i know that i have to let 'x^2' equal to ' 9tan t' , but I DONT KNOW WHY. Once again, the only reason why I was able to get tthe right answer was by looking at the multiple choice answers and figuring it out from there...
I know how to do the rest after this point, I only someone to explain me how is it that we figure out to let 'x^2= 9tan t'
2007-02-20 20:19:00 · 3 answers · asked by Sir Excalibur 2 in Science & Mathematics ➔ Mathematics
you have given integral of x/(81+x^4)
it is inconvinent to do it without substitution
look at denominator (9^2+x^4) you know 1+tan^2t=sec^2t
hence if you take x^4=81 tan^2t (or x^2=9tant)
it would be easy and denominator would become 81sec^2t
2007-02-20 20:32:42 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Set u=2x+x^2 and du=2+2x you need to factor du to be 2(x+a million), then the (x+a million) indoors the numerator can cancel out and additionally you're left with needed of u^(a million/2) over 2. Then integrate like prevalent and plug u lower back in.
2016-10-16 03:59:57 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Please see my addendum that I put at the bottom of my answer to your original posting.
2007-02-20 20:27:04 · answer #3 · answered by Northstar 7 · 1⤊ 0⤋