Integrate a transcendental function given by a power series?

[bmmmburns (Marvin Ray Burns A.G.S. (cum laude))]

NSum uses floating point arithmetic, so it doesn’t have to worry about the algebra!

I think the code can be sped up even more!

Mathematica is really very fast, if you use it right. See how much I sped up the MRB constant record computations !!!