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1 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 | --Copyright The Numerical Algorithms Group Limited 1994.
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-- some genus 0 integrations
y := sqrt(a * x + b)
integrate(%,x)
x * y
integrate(%,x)
z := sqrt(a**2 - x**2)
1 / z
integrate(%,x)
x**2 * z
integrate(%,x)
x**3 / (a+b*x)**(1/3)
integrate(%,x)
1 / (x**3 * (a+b*x)**(1/3))
integrate(%,x)
-- examples of transcendentals over a curve of genus 0
x / (y + y**2) + log(y + 1)
integrate(%,x)
(2 + 1/sqrt(x)) * cos(x + sqrt x)
integrate(%,x)
-- one which does not have an elementary integral
log(1 + y) / x
integrate(%,x)
-- integrals of hyperbolic trigs are returned in terms of hyperb. trigs.
(sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b))))
integrate(%,x)
-- examples of genus 0 functions presented as transcendentals
tan(atan(x)/2)
integrate(%,x)
tan(atan(x)/3)
integrate(%,x)
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