Generating tables of derivatives and integrals

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Contents

Description

This example shows how SymPy can be used to automatically generate tables of, for instance, derivatives and integrals. We print the output in TeX (replacing the $-signs in the TeX output with <math></math>-tags for display on the wiki). 

from sympy import *
 
def derivative_table(functions, x):
    for f in functions:
        s = printing.latex(Derivative(f, x) == diff(f, x))
        print ":<math>" + s[1:-1] + "</math>", "\n"
 
def integral_table(functions, x):
    for f in functions:
        s = printing.latex(Integral(f, x) == integrate(f, x))
        print ":<math>" + s[1:-1] + "</math>", "\n"
 
var('x')
 
print "===Derivatives==="
derivative_table([cos(x)/(1 + sin(x)**i) for i in range(1, 5)], x)
 
print "===Integrals==="
integral_table([x**i * exp(i*x) for i in range(1, 5)], x)

Output

Derivatives

\frac{\partial}{\partial x}\left(\frac{\operatorname{cos}\left(x\right)}{1 + \operatorname{sin}\left(x\right)}\right) = - \frac{\operatorname{sin}\left(x\right)}{1 + \operatorname{sin}\left(x\right)} - \frac{\operatorname{cos}^{2}\left(x\right)}{\left(1 + \operatorname{sin}\left(x\right)\right)^{2}}
\frac{\partial}{\partial x}\left(\frac{\operatorname{cos}\left(x\right)}{1 + \operatorname{sin}^{2}\left(x\right)}\right) = - \frac{\operatorname{sin}\left(x\right)}{1 + \operatorname{sin}^{2}\left(x\right)} - 2 \frac{\operatorname{c os}^{2}\left(x\right) \operatorname{sin}\left(x\right)}{\left(1 + \operatorname{sin}^{2}\left(x\right)\right)^{2}}
\frac{\partial}{\partial x}\left(\frac{\operatorname{cos}\left(x\right)}{1 + \operatorname{sin}^{3}\left(x\right)}\right) = - \frac{\operatorname{sin}\left(x\right)}{1 + \operatorname{sin}^{3}\left(x\right)} - 3 \frac{\operatorname{c os}^{2}\left(x\right) \operatorname{sin}^{2}\left(x\right)}{\left(1 + \operatorname{sin}^{3}\left(x\right)\right)^{2}}
\frac{\partial}{\partial x}\left(\frac{\operatorname{cos}\left(x\right)}{1 + \operatorname{sin}^{4}\left(x\right)}\right) = - \frac{\operatorname{sin}\left(x\right)}{1 + \operatorname{sin}^{4}\left(x\right)} - 4 \frac{\operatorname{c os}^{2}\left(x\right) \operatorname{sin}^{3}\left(x\right)}{\left(1 + \operatorname{sin}^{4}\left(x\right)\right)^{2}}

Integrals

\int x {e}^{x}\,dx = - {e}^{x} + x {e}^{x}
\int {x}^{2} {e}^{2 x}\,dx = \frac{1}{4} {e}^{2 x} + \frac{1}{2} {x}^{2}{e}^{2 x} - \frac{1}{2} x {e}^{2 x}
\int {x}^{3} {e}^{3 x}\,dx = - \frac{2}{27} {e}^{3 x} - \frac{1}{3} {x}^{2} {e}^{3 x} + \frac{1}{3} {x}^{3} {e}^{3 x} + \frac{2}{9} x {e}^{3 x}
\int {x}^{4} {e}^{4 x}\,dx = \frac{3}{128} {e}^{4 x} - \frac{3}{32} x {e}^{4 x} - \frac{1}{4} {x}^{3} {e}^{4 x} + \frac{1}{4} {x}^{4} {e}^{4 x} + \frac{3}{16} {x}^{2} {e}^{4 x}
Retrieved from "http://wiki.sympy.org/wiki/Generating_tables_of_derivatives_and_integrals"
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