anonymous
  • anonymous
what will be the integration of 1/(1+x²)½ along x?
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.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[\int\limits 1/(1+x ^{2})^{1/2}\] it will be \[\ln (1 + x ^{2})^{1/2}\]
anonymous
  • anonymous
you know that when the numerator is the derivative of the dominator then the integration is ln "dominator" :)
anonymous
  • anonymous
but the derivative of denominator should be there in the numerator

Looking for something else?

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

More answers

anonymous
  • anonymous
\[x= \tan \theta\]
anonymous
  • anonymous
ok , the derivative of (x^2 )^1/2 is 1/2 (2x) so 2 cancel the other 2 :)
anonymous
  • anonymous
and for natural log, exponent should be 1
anonymous
  • anonymous
\[\int\limits 1/x= \ln x\]
anonymous
  • anonymous
if the exponent is other than 1, we use power rule
anonymous
  • anonymous
yeah but we can't multiply it with 2x so ln(1+x²)½ is not the right answer
anonymous
  • anonymous
\[d x= \sec^2 \theta d \theta\]
anonymous
  • anonymous
i think its correct .. anyways good luck ..
anonymous
  • anonymous
\[\int\limits \sec^2 \theta/(\sqrt{1+\tan^2 \theta} )\]
anonymous
  • anonymous
\[\int\limits \sec^2\theta/\sec \theta d \theta\]
anonymous
  • anonymous
\[\int\limits \sec \theta d \theta\]
anonymous
  • anonymous
\[\ln (\sec \theta + \tan \theta) +C\]
anonymous
  • anonymous
by backward substitution \[\tan \theta =x\]
anonymous
  • anonymous
yeah that will give us integration of secθ that is ln(secθ+tanθ) and by substituting and we will get probably get ln(sec(tan^-x)+x)
anonymous
  • anonymous
\[\sec \theta =\sqrt{1+x^2}\]
anonymous
  • anonymous
thanks for the help i have some questions on multiple integral usage in finding area and volume. Anyone please help me
anonymous
  • anonymous
post it as a new Q,some one would surly look at it :)
anonymous
  • anonymous
Uzma are you from Pakistan?
anonymous
  • anonymous
ahaa ! ok waiting ur new Qs :)
anonymous
  • anonymous
yes :)
anonymous
  • anonymous
Can you please tell me your qualification and city
anonymous
  • anonymous
what would u do with that :)
anonymous
  • anonymous
nothing just to guess the level of your understanding mathematics
anonymous
  • anonymous
mathematics is as vast, that one can hardly grasp even one area

Looking for something else?

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