Luigi0210
  • Luigi0210
How would you approach this integral?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Luigi0210
  • Luigi0210
\(\Huge \int \frac{x}{\sqrt{x^4-1}} dx \)
BloomLocke367
  • BloomLocke367
I wish I could help :O
anonymous
  • anonymous
Here's my thinking, step by step: I'd start by looking for substitutions. 1. Try u = x^4. Tried this substitution but it didn't help much. 2. Try u = x^2. This gives integral of 0.5*(u^2-1)^-0.5. Helpful. Let's take this forward. 3. Notice the u^2 - 1 on the bottom. If I substitute u = cosh(theta), then u^2-1 becomes sinh^2 (theta). Furthermore, the u*du on the top becomes sinh(theta)d(theta), which cancels a bit. Nice! 4. Let me work the next bit out on paper, then I'll get back to you... :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Oops, I missed a square root. In fact, step 3 gives sinh(u)/sinh(u), which is just 1. So step four is just integrate 1 w.r.t. theta, which gives theta.
anonymous
  • anonymous
Now unravelling the substitutions in reverse order, u = x^2 and u = cosh(theta). So theta becomes arccosh(u) which is arccosh(x^2). So the final answer is arccosh(x^2), I think!
anonymous
  • anonymous
(I can write this up properly with the maths/equation/LaTeX notation, if you want)
Luigi0210
  • Luigi0210
Thanks for your input, it was arccosh (x^2) +C actually :D I see what I did wrong tho.. I used a bad substitution :/
anonymous
  • anonymous
Oops, yes, I always forget the +C ! Substitutions are a pain, it's often a case of trial and error. Apparently it gets better with "experience", but I reckon that probably means doing enough practice problems to remember most of them :/
Luigi0210
  • Luigi0210
True, thanks for your help, really appreciate it (:
anonymous
  • anonymous
No problem! :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.