AmTran_Bus
  • AmTran_Bus
Can someone check this integration?
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.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
AmTran_Bus
  • AmTran_Bus
anonymous
  • anonymous
What have you tried? By parts?
AmTran_Bus
  • AmTran_Bus
Sorry, just got back to this page. Let me show you.

Looking for something else?

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

More answers

AmTran_Bus
  • AmTran_Bus
So if you say |dw:1434570936513:dw|
AmTran_Bus
  • AmTran_Bus
That is after IBP
AmTran_Bus
  • AmTran_Bus
Then can't you do a sub?
anonymous
  • anonymous
So it looks like you set \(u=\ln x\) and \(dv=\dfrac{x}{\sqrt{x^2-1}}\,dx\). A trig substitution might work. Try \(x=\sec u\).
AmTran_Bus
  • AmTran_Bus
That give|dw:1434571156177:dw|
anonymous
  • anonymous
Let's see... \[\int\frac{\sqrt{x^2-1}}{x}\,dx=\int\frac{\sqrt{\sec^2u-1}}{\sec u}\sec u\tan u\,du=\int \tan^2u\,du\] Now a trig identity will work well here: \[\tan^2u=\sec^2u-1\] and you know the antiderivative of \(\sec^2u\).
AmTran_Bus
  • AmTran_Bus
Yes, so does that not give
AmTran_Bus
  • AmTran_Bus
|dw:1434571377468:dw|
anonymous
  • anonymous
That's right.
AmTran_Bus
  • AmTran_Bus
Moving on then, I end up at the end getting something different :(|dw:1434571498405:dw|
anonymous
  • anonymous
\(\ln x(x-1)\) should be \((\ln x-1)\).
AmTran_Bus
  • AmTran_Bus
Whoops! Ok. But does that match any of those possible answers, or have we made a mistake?
anonymous
  • anonymous
Other than that, your solution is right. I suspect a typo in the answer choices.
AmTran_Bus
  • AmTran_Bus
Thanks. I wonder if any are equivalent?
AmTran_Bus
  • AmTran_Bus
Because I have not ever had a problem where they have made a mistake before.
anonymous
  • anonymous
You can differentiate the answer choices to check. The second one can be eliminated right away since it doesn't generate any log terms.
AmTran_Bus
  • AmTran_Bus
Ok. Thanks so much!
anonymous
  • anonymous
You're welcome!

Looking for something else?

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