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AndrasBest ResponseYou've already chosen the best response.1
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
 2 years ago

nubeerBest ResponseYou've already chosen the best response.0
hmmm ya i also reached at this point but what after this?
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
thinking of the next substitution, maybe some trig function
 2 years ago

nubeerBest ResponseYou've already chosen the best response.0
hmm yes i think that would be tan but how and why
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
I know! Recall that tan^2(x)+1=sec^2(x)
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
so we need to make 9tan^2(x) from u to get 9(tan^2(x)+1)
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
let u=3tan(z) du=3sec^2(z) dz
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
So the integral will be: 3sec^2(z)/3sec(z)=sec(z)
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
What the integral of secz? log(tanz+secz) (just looked it up)
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
we have u=3tanz expressing z=tan^1(u/3)
 2 years ago

nubeerBest ResponseYou've already chosen the best response.0
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
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
because if it is 3tan than (3tan)^2=9tan^2(x) so we can factor out 9 to get 9(tan^2(x)+1)
 2 years ago

nubeerBest ResponseYou've already chosen the best response.0
ohh so just that was the reason to put 3?
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
Hope it helped, now you just need to plug back the z and u to get x
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.0
do you know about hyperbolic functions ?
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.0
and this is a elementary problem no need to think hard on this one
 2 years ago

AndrasBest ResponseYou've already chosen the best response.1
e^x+e^x/2 how would that help?
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.0
\[\frac{d}{dx}\operatorname{arsinh}(x) =\frac{1}{\sqrt{x^{2}+1}}\]
 2 years ago
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