RE: Sovling integrals: non-algebraic???

• To: mathgroup at smc.vnet.net
• Subject: [mg35394] RE: [mg35369] Sovling integrals: non-algebraic???
• From: "DrBob" <majort at cox-internet.com>
• Date: Wed, 10 Jul 2002 02:22:32 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I'm sure that equation has no closed form solution; hence it's no
surprise if Mathematica can't find one.  MANY problems have no solution.
Real world problems almost NEVER have a solution.  It's often your task
to simplify your problem intelligently until it becomes a problem you
can solve.

The following steps transform the problem to something less ugly:

int = Integrate[c x^d, {x, a, b}];
eqn = int == y
eqn2 = #(1 + d)/c & /@ eqn // Simplify
eqn3 = eqn2 /. d -> f - 1
eqn4 = # - eqn3[[2, 1]] & /@ eqn3
eqn5 = eqn4 /. y/c -> h

If you can solve for f, use d==f-1.

That's one equation in four unknowns, and it's transcendental in the one
you want to solve for, so...

Good luck!

Bobby Treat

-----Original Message-----
From: Björn [mailto:sirepumpkin at hotmail.com]
To: mathgroup at smc.vnet.net
Subject: [mg35394] [mg35369] Sovling integrals: non-algebraic???

Hello!

I can't make Mathematica solve an expression for a variable which is
inside an integral. Integrals are of the form:
Integrate[f, {x, xmin, xmax}]

And my expression is of the kind:
Solve[Integrate[(c x^d), {x, a, b}] == y, d]

Now, Mathematica can solve for a, b and c. But it cannot solve for d.
Why?

It gives me the message:
"The equations appear to involve the variables to be solved for in an
essentially non-algebraic way."

If I try SolveAlways[Integrate[c x^d, {x, a, b}] == y, d],
I get the message:
"The expression (a^(1 + d)) involves unknowns in more than one
argument, so inverse functions cannot be used."

(It isn't mathematically impossible, right?)

Most thankful for any help!

```

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