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wioBest ResponseYou've already chosen the best response.0
I would try to factor the quadratic or something.
 one year ago

matrickedBest ResponseYou've already chosen the best response.0
u have to firs express numerator as A(diif of denom )+B where A and B are constatnts to be dtermined thus A(2x+4) +B =x+3
 one year ago

LogicalAppleBest ResponseYou've already chosen the best response.1
After you factor the denominator you will get an expression that lends itself (not too nicely) to a few layers of substitution. I am getting a rather complicated trigonometric answer when I do it.
 one year ago

matrickedBest ResponseYou've already chosen the best response.0
equating coefficient on both sides we have 2A=1 or A=1/2 and 4A+B=3 or B=1 thus (x+3)= 1/2 (2x+4) +1 hence reqd integ breaks down to two as 1/2 (2x+4)/(x^2+4x+5) +1 /((x^2+4x+5) let I =integral of 1/2 (2x+4)/(x^2+4x+5) and J = integral of 1 /((x^2+4x+5) now one has to eavaluate first I and J
 one year ago

wioBest ResponseYou've already chosen the best response.0
Actually looks like you have to complete the square of the denominator.
 one year ago

LogicalAppleBest ResponseYou've already chosen the best response.1
Right, after completing the square on the bottom you can obtain an equivalent form where u = x + 2: integrate (u + 1) / sqrt(u^2 + 1) du Still complicated from here though.
 one year ago

wioBest ResponseYou've already chosen the best response.0
\[(a+b)^2 = a^2 +2ab + b^2 \\ a = x \\ b = ? \]
 one year ago

matrickedBest ResponseYou've already chosen the best response.0
for I substitute (x^2+4x+5)=z or (2x+4)dx=dz hence I =1/2 (inegral of dz/z) =1/2 lnz +c1 or I=1/2 ln (x^2+4x+5)+c1
 one year ago

matrickedBest ResponseYou've already chosen the best response.0
Now for J one has to complete sqaures thus (x^2+4x+5)=(x^2+4x+4+1)=(x+2)^2 +1
 one year ago

matrickedBest ResponseYou've already chosen the best response.0
J= integral of 1/((x+2)^2 +1) = tan^1(x+2) +c2
 one year ago

matrickedBest ResponseYou've already chosen the best response.0
thus reqd answer is 1/2 ln (x^2+4x+5) + tan^1(x+2) +c [ where c=c1+c2 all integrating constant]
 one year ago

LogicalAppleBest ResponseYou've already chosen the best response.1
I think the derivative of the function you provided yields (x + 3) / (x^2 + 4x + 5) instead of (x + 3) / sqrt(x^2 + 4x + 5). I got sqrt(x^2 + 4x + 5) + ln (x + 2 + sqrt( (x + 2)^2 + 1)) for the final answer. Can you double check this?
 one year ago

drake_96Best ResponseYou've already chosen the best response.0
@LogicalApple :you are right.
 one year ago
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