Integration and ODEs (scipy.integrate)

Integrating functions, given function object

quad(func, a, b[, args, full_output, ...]) Compute a definite integral.
dblquad(func, a, b, gfun, hfun[, args, ...]) Compute a double integral.
tplquad(func, a, b, gfun, hfun, qfun, rfun) Compute a triple (definite) integral.
nquad(func, ranges[, args, opts]) Integration over multiple variables.
fixed_quad(func, a, b[, args, n]) Compute a definite integral using fixed-order Gaussian quadrature.
quadrature(func, a, b[, args, tol, rtol, ...]) Compute a definite integral using fixed-tolerance Gaussian quadrature.
romberg(function, a, b[, args, tol, rtol, ...]) Romberg integration of a callable function or method.

Integrating functions, given fixed samples

cumtrapz(y[, x, dx, axis, initial]) Cumulatively integrate y(x) using the composite trapezoidal rule.
simps(y[, x, dx, axis, even]) Integrate y(x) using samples along the given axis and the composite
romb(y[, dx, axis, show]) Romberg integration using samples of a function.

See also

scipy.special for orthogonal polynomials (special) for Gaussian quadrature roots and weights for other weighting factors and regions.

Integrators of ODE systems

odeint(func, y0, t[, args, Dfun, col_deriv, ...]) Integrate a system of ordinary differential equations.
ode(f[, jac]) A generic interface class to numeric integrators.
complex_ode(f[, jac]) A wrapper of ode for complex systems.