Math Is Fun Forum

Agnishom

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From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

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Indefinite Integrals

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

zetafunc

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Registered: 2014-05-21

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Re: Indefinite Integrals

Use partial fractions. The integrand can be written as a sum of multiples of 1/x^6, 1/x^4, 1/x^2 and 1/(x^2 + 1). These can then of course be integrated term by term.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

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Re: Indefinite Integrals

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

zetafunc

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Registered: 2014-05-21

Posts: 2,441

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Re: Indefinite Integrals

Let x = u^2. You'll then end up with an integrand involving a linear term k*u in the numerator, and a quadratic under a square root in the denominator. Then use a trig substitution involving sec and tan, so that your integrand ends up being of the form sec(y)*(1 + sec(y)) = sec(y) + sec²(y) -- and this is something you can integrate term-by-term.

Last edited by zetafunc (2016-01-04 05:32:07)

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Indefinite Integrals

Thanks, it works.

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.