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Andras
 3 years ago
Best ResponseYou've already chosen the best response.1This 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
 3 years ago
Best ResponseYou've already chosen the best response.0hmmm ya i also reached at this point but what after this?

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

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

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

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

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

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

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

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

nubeer
 3 years ago
Best ResponseYou've already chosen the best response.0thanks 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

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

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

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

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.0do you know about hyperbolic functions ?

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

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

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