Re: Integral problem
- To: mathgroup at smc.vnet.net
- Subject: [mg27888] Re: [mg27874] Integral problem
- From: BobHanlon at aol.com
- Date: Fri, 23 Mar 2001 04:31:08 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
expr = (x^3/(x^4+x^2+1));
soln1 = Simplify[Integrate[expr, x]]
((2 - 2*I*Sqrt[3])*ArcTan[(x^2 - 1)/(Sqrt[3]*(x^2 + 1))] +
4*ArcTan[(x^2 + 2)/(Sqrt[3]*x^2)] +
(3*I + Sqrt[3])*Log[x^4 + x^2 + 1])/(4*(3*I + Sqrt[3]))
Simplify[D[soln1, x]] == expr
True
soln2 = 1/4 Log[x^4+x^2+1]-(Sqrt[3]/6) ArcTan[(2x^2+1)/Sqrt[3]];
Simplify[D[soln2, x]] == expr
True
They differ by a constant.
c = soln1 - soln2 /. x -> 1.
0.4534498410585545 - 0.26179938779914946*I
And @@ Table[soln1 - soln2 \[Equal] c, {x, 0.1, 2, 0.1}]
True
Bob Hanlon
In a message dated 2001/3/22 4:50:49 AM, jml at accessinter.net writes:
>Well in my calculus class, I need to integrate the following expression:
>(x^3/(x^4+x^2+1))dx, I solve the integral with Mathematica, but a few
>classmates got a different answer using other symbolic algebra
>system, the answers are totally different, the answer that my
>classmates got is:
>1/4 Ln(x^4+x^2+1)-(Sqrt(3)/6) ArcTg((2x^2+1)/Sqrt(3)) is this the
>correct answer??