### Table Of Contents

- Integration and ODEs (`scipy.integrate`)
  - Integrating functions, given function object
  - Integrating functions, given fixed samples
  - Integrators of ODE systems

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# 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, full_output]) | 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.
`quad_explain`([output]) | Print extra information about integrate.quad() parameters and returns.
`newton_cotes`(rn[, equal]) | Return weights and error coefficient for Newton-Cotes integration.
`IntegrationWarning` | Warning on issues during integration.

## Integrating functions, given fixed samples

`trapz`(y[, x, dx, axis]) | Integrate along the given axis using the composite trapezoidal rule.
`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.

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.
`solve_bvp`(fun, bc, x, y[, p, S, fun_jac, ...]) | Solve a boundary-value problem for a system of ODEs.