

I somehow got off on a tangent graphing some orthogonal polynomials, and then
went the rest of the way and implemented the GaussLaguerre integration method.
Amazingly, it "works", and I get a ballpark answer for all of the equations that
I've found exact answers for the integrations  however I feel like I ought to
be getting far more accurate answers. Like, to 6 decimal places or more.
https://thoughtsoncoding.com/2019/04/25/numericalmethodsincpppart2gausslegendreintegration/
Using Laguerre polynomial level 5
Integral of (5/(pow(e, pi)2)) * exp(2*_X) * cos(_X) dx from: [0.000] to:
[1.571] = 0.9914612 Actual answer = 1.0000000
Integral of pow(x,2) + 1 dx from: [0.000] to: [2.000] = 4.6207326
Actual answer = 4.6666667
Integral of pow(x,2) + pow(x,2) dx from: [1.000] to: [2.000] =
2.8064163 Actual answer = 2.8333333
Integral of 6*pow(x,2)  5*x + 2 dx from: [3.000] to: [1.000] =
83.1007807 Actual answer = 84.0000000
Integral of sqrt (x) * (x2) dx from: [4.000] to: [0.000] = 2.0968530
Actual answer = 2.1333333
Integral of (2*pow(x,5)  x + 3) / pow(x,2) dx from: [1.000] to: [2.000]
= 8.2261864 Actual answer = 8.3068528
Integral of 4*x  6*pow(pow(x,2), 1/3) dx from: [0.000] to: [1.000] =
1.5870838 Actual answer = 1.6000000
Integral of 2*sin(x)  5*cos(x) dx from: [0.000] to: [1.047] =
3.2996419 Actual answer = 3.3301270
Integral of 3/exp(x)  1/3*x dx from: [20.000] to: [1.000] =
2.0601572 Actual answer = 2.1022157
Integral of abs(3x5) dx from: [0.000] to: [3.000] = 6.7223530
Actual answer = 6.8333333
Integral of 4*pow(x,4)  pow(x,2) + 1 dx from: [2.000] to: [2.000] =
41.3601713 Actual answer = 49.8666667
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