Nodes and Weights of Tanh-Sinh Calculator

Calculates the nodes and weights of the Tanh-Sinh integration.

 $\normal{\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx\simeq{\large\int_{-t_a}^{\hspace{25}t_a}}f(x(t))x'(t)dt\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\\ nodes\\\hspace{20} x_i=tanh(\frac{\pi}{2}sinh(t_i)),\hspace{10}t_i=-t_a+(i-1)h\\[10]\ weights\\\hspace{20} w_i={\large\frac{\frac{\pi}{2}cosh(t_i)}{cosh^2(\frac{\pi}{2}sinh(t_i))}}h,\hspace{10}h={\large\frac{2t_a}{n-1}}\\\vspace{10}$
 nodes half all order n 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 n=2,3,4,..,100 ta auto manual -->
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Tanh-Sinh\ integration\\\hspace{5}(1)\hspace{1} {\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx={\large\int_{\small -\infty}^{\hspace{25}\small \infty}}f(x(t))x'(t)dt\\\hspace{90}\simeq{\large\int_{-t_a}^{\hspace{25}t_a}}f(x(t))x'(t)dt\\\hspace{140}x(t)=tanh(\frac{\pi}{2}sinh(t))\\\hspace{140}x'(t)={\large\frac{\frac{\pi}{2}cosh(t)}{cosh^2(\frac{\pi}{2}sinh(t))}}\\(2)\ Trapezoid\\\hspace{20} {\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\\hspace{10}nodes\\\hspace{20} x_i=tanh(\frac{\pi}{2}sinh(t_i)),\hspace{10}t_i=-t_a+(i-1)h\\[10]\hspace{10}weights\\\hspace{20} w_i={\large\frac{\frac{\pi}{2}cosh(t_i)}{cosh^2(\frac{\pi}{2}sinh(t_i))}}h,\hspace{10}h={\large\frac{2t_a}{n-1}}\\$

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