I try to find the exact (symbolic) value of

(-2*sqrt(7)-4)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))^2+4*EllipticE(-(1/8)*sqrt(2)*(-3+sqrt(7)))*sqrt(7)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))

I tried 'simplify' with different options and 'convert'. It would be pi=3.141... as numerical approximation suggests.

Many thanks.

It is given 

   xⁿ (n x - n - x) / (x-1)² + x / (x-1)²  , n is a (symbolic) positive integer.

I want to transform it into

n xⁿ⁺¹ / (x-1) - x (xⁿ-1) / (x-1)². 

How is it possible?

I tried the  simplify, convert (parfrac), collect, combine, expand,  with/without assuming.

Thanks in advance.

I want to find the solution in a special form.
How can I do it?
Here is what I tried:

(Maple)

(Maple)


In the left hand side u_1 is not changed in  D(u_1).
I want to substitute and evalute (differentiate) it.

Thanks,  Sandor

I can not interpret this answer.

I think here I is the complex unit.

> assume(a < 0);
> convert(cosh(sqrt(a)), sincos);
print(`output redirected...`); # input placeholder
/ (1/2)\
cos\(-a) /

This is what I expected.

Now

> assume(L > 0);
> assume(K > 0);
> assume(mu > 0);
> assume(mu^2 < 4*L*k);
> assume(t > 0);
> convert(cosh((1/2)*t*sqrt(mu^2-4*L*k)/L), sincos);
print(`output redirected...`); # input placeholder
/ (1/2)\
| / 2 \ |
|t \mu - 4 L k/ |
cosh|--------------------|
\ 2 L /

I wanted to obtain again the cos function. Could someone help me?
(What is the reason that convert does not work "well" in later case?)

 Thanks,  Sandor