manualintegrate.py 文件源码

def manualintegrate(f, var):
    """manualintegrate(f, var)

    Compute indefinite integral of a single variable using an algorithm that
    resembles what a student would do by hand.

    Unlike ``integrate``, var can only be a single symbol.

    Examples
    ========

    >>> from sympy import sin, cos, tan, exp, log, integrate
    >>> from sympy.integrals.manualintegrate import manualintegrate
    >>> from sympy.abc import x
    >>> manualintegrate(1 / x, x)
    log(x)
    >>> integrate(1/x)
    log(x)
    >>> manualintegrate(log(x), x)
    x*log(x) - x
    >>> integrate(log(x))
    x*log(x) - x
    >>> manualintegrate(exp(x) / (1 + exp(2 * x)), x)
    atan(exp(x))
    >>> integrate(exp(x) / (1 + exp(2 * x)))
    RootSum(4*_z**2 + 1, Lambda(_i, _i*log(2*_i + exp(x))))
    >>> manualintegrate(cos(x)**4 * sin(x), x)
    -cos(x)**5/5
    >>> integrate(cos(x)**4 * sin(x), x)
    -cos(x)**5/5
    >>> manualintegrate(cos(x)**4 * sin(x)**3, x)
    cos(x)**7/7 - cos(x)**5/5
    >>> integrate(cos(x)**4 * sin(x)**3, x)
    cos(x)**7/7 - cos(x)**5/5
    >>> manualintegrate(tan(x), x)
    -log(cos(x))
    >>> integrate(tan(x), x)
    -log(sin(x)**2 - 1)/2

    See Also
    ========

    sympy.integrals.integrals.integrate
    sympy.integrals.integrals.Integral.doit
    sympy.integrals.integrals.Integral
    """
    return _manualintegrate(integral_steps(f, var))