Can't seem to get this integration to work. s, n, b, b, l are all constants.

In[1]:= Integrate[Sin[n Pi x / l] (1 + s x - Sqrt[(x - Sqrt[1 - b])^2 + b]), {x, 0,l}, Assumptions -> Element[x, Reals]]

output is just the input, which indicates to me that mathematica doesn't like it, I'm unsure why.

Any help is greatly appreciated

  • 5
    $\begingroup$ Why do you expect that there is a closed form solution? Not all integrals can be expressed in closed form. $\endgroup$ – Henrik Schumacher Mar 30 at 15:26

I think you have to set constants values for your Constants so the integral can be evaluated. Otherwise it return error for solution to set constant values.

n = 1;
s = 1;
l = 1;
b = 1;

f[x_] := Refine[
  Sin[n Pi x/l] *(1 + s x - Sqrt[(x - Sqrt[1 - b])^2 + b]), 
  Assumptions -> {Element[x, Reals]}

Integrate[Simplify[f[x]], {x, 0, 1}] // N

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