Re: Integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg14776] Re: Integrals
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Sat, 14 Nov 1998 03:08:06 -0500
• References: <7256fr\$870@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

jose andres garcia wrote in message <7256fr\$870 at smc.vnet.net>...
>I need help to resolve this two integrals and if it's posible show the
>solution step by step.
>
>    Int((sqrt(x^2-5x+9)-2x^2+x)/((x+1)sqrt(x^2-5x+9))
>
>
>     Int((x^4-7x+2)/((x^2)(sqrt(5x^2+x-10))))
>

Jose,
Here are the answers that Mathematica gives,

Integrate[(Sqrt(x^2 - 5x + 9) - 2x^2 + x)/((x + 1)Sqrt[x^2 - 5x + 9]) ,
x]

(-2 + Sqrt)*Sqrt[9 - 5*x + x^2] + 1/2*(-4 - 7*Sqrt)*
ArcSinh[(-5 + 2*x)/Sqrt[11]] + Sqrt[3/5]*(-1 + 5*Sqrt)*
Log[1 + x] - Sqrt[3/5]*(-1 + 5*Sqrt)*
Log[23 - 7*x + 2*Sqrt[15]*Sqrt[9 - 5*x + x^2]]

Integrate[(x^4 - 7x + 2)/((x^2)(Sqrt(5x^2 + x - 10))), x]

1/Sqrt*(1/(5*x) + x/5 - 2/25*Sqrt[67/3]*
ArcTanh[(1 + 10*x)/(Sqrt[3]*Sqrt[67])] +
(17*Log[x])/25 - 9/25*Log[-10 + x + 5*x^2])

Allan

---------------------
Allan Hayes
Mathematica Training and Consulting
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

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