If I have an expression like this

f:=ln((1-x)^2*(x+1)^2/((-I*x-I+sqrt(-x^2+1))^2*(I*x+I+sqrt(-x^2+1))^2))

maple has trouble to simplify the argument.

In particular is it possible to apply expand() only to the denominator?

This is meant in general, so if I have many terms with expressions like this (possibly of products with other functions in each term), I want this simplification to be done termwise for the arguments of the functions.

Expanding the fraction doesn't work as in frontend(expand, [f]).

This is not a problem per se, but more to understand the background.

restart;

f := polylog(2, -x);

int(f/(x+1), x);

convert(f, dilog);

int(%/(x+1), x)

The integration of the polylog maple is not capable of doing, but after converting to dilog it finds an anti derivative.

That leads to the question, why is dilog as a separate to polylog(2,*) implemented anyway? Why couldn't it all be done with the more general polylog function?

I'm also wondering why maple has difficulties to integrate

int(dilog(x+1)/(x+a),x)

for general a.

Hello,

I have this error I'm not sure how to solve

restart;

`assuming`([simplify(int(ln(1+x)^3/(x+a), x = 0 .. 1))], [a > 0]);

combine(expand((eval(%, a = I)+eval(%, a = -I))*(1/2)))

What is the precise problem here?

restart;
Digits := 15;

b := -I;

a := sqrt(2);

epsilon := 1;

f := proc (t) options operator, arrow; evalf(Int(exp(I*k*t)/((1+a^2*sin(k)^2)*(k-b)^epsilon), k = -infinity .. infinity)) end proc;

f(1.3)

I tried different methods like _d01amc, but either I have this error:

Error, (in evalf/int) NE_QUAD_NO_CONV:
  The integral is probably divergent or slowly convergent.

or it takes forever.

I also tried to map the interval to some finite length (k=tan(u)), but then I get

Error, (in evalf/int) NE_QUAD_BAD_SUBDIV:
  Extremely bad integrand behaviour occurs around the
  sub-interval (-1,5707963e+000, -1,5707963e+000 ).

disgusting integrand?

restart;

Digits := 32;

t0 := 1;

eq := 1-w*v^2-2*v*exp(-t/v);

equ := eval(eq, v = -t/ln(u));

us := solve(eval(equ, t = t0), u);

vs := -t0/ln(us);

plot(Re(vs), w = 0 .. 10, view = 0 .. 1)

I want to plot the solution of this equation, but it doesn't quite work. I tried to transform it, because I thought the singularity in the denominator of the exponential causes the issues.

any suggestions?