nubeer
  • nubeer
integrate (1/(x^2+8x +25 )^0.5)
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
This is a hard one x^2+8x+25=(x+4)^2+9 so use sub u=x+4 du=dx New integral: 1/(u^2+9)^0.5
nubeer
  • nubeer
hmmm ya i also reached at this point but what after this?
anonymous
  • anonymous
thinking of the next substitution, maybe some trig function

Looking for something else?

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

More answers

nubeer
  • nubeer
hmm yes i think that would be tan but how and why
anonymous
  • anonymous
I know! Recall that tan^2(x)+1=sec^2(x)
anonymous
  • anonymous
so we need to make 9tan^2(x) from u to get 9(tan^2(x)+1)
anonymous
  • anonymous
let u=3tan(z) du=3sec^2(z) dz
anonymous
  • anonymous
So the integral will be: 3sec^2(z)/3sec(z)=sec(z)
anonymous
  • anonymous
What the integral of secz? log(tanz+secz) (just looked it up)
anonymous
  • anonymous
we have u=3tanz expressing z=tan^-1(u/3)
nubeer
  • nubeer
thanks man.. well pretty much hit the answer but can u explain this 1 step let u=3tan(z) du=3sec^2(z) dz.. why we suppose 3 tan(z) why not just tan
anonymous
  • anonymous
because if it is 3tan than (3tan)^2=9tan^2(x) so we can factor out 9 to get 9(tan^2(x)+1)
nubeer
  • nubeer
ohh so just that was the reason to put 3?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Hope it helped, now you just need to plug back the z and u to get x
anonymous
  • anonymous
do you know about hyperbolic functions ?
anonymous
  • anonymous
sinhx ?
anonymous
  • anonymous
and this is a elementary problem no need to think hard on this one
anonymous
  • anonymous
e^x+e^-x/2 how would that help?
Zarkon
  • Zarkon
\[\frac{d}{dx}\operatorname{arsinh}(x) =\frac{1}{\sqrt{x^{2}+1}}\]

Looking for something else?

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