# 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 Simpson’s rule. romb(y[, dx, axis, show]) Romberg integration using samples of a function.

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.