sage: from sage.symbolic.integration.integral import definite_integral sage: definite_integral(sin(x),x,0,pi) 2
sage: from sage.symbolic.integration.integral import indefinite_integral sage: indefinite_integral(log(x), x) #indirect doctest x*log(x) - x sage: indefinite_integral(x^2, x) 1/3*x^3 sage: indefinite_integral(4*x*log(x), x) 2*x^2*log(x) - x^2 sage: indefinite_integral(exp(x), 2*x) 2*e^x
esempi:
sage: x = var('x') sage: h = sin(x)/(cos(x))^2 sage: h.integral(x) 1/cos(x
sage: f = x^2/(x+1)^3 sage: f.integral(x) 1/2*(4*x + 3)/(x^2 + 2*x + 1) + log(x + 1)
sage: f = x*cos(x^2) sage: f.integral(x, 0, sqrt(pi)) 0 sage: f.integral(x, a=-pi, b=pi) 0
sage: f(x) = sin(x) sage: f.integral(x, 0, pi/2) 1
sage: y=var('y') sage: integral(sin(x), x) -cos(x) sage: integral(sin(x), y) y*sin(x) sage: integral(sin(x), x, pi, 2*pi) -2 sage: integral(sin(x), y, pi, 2*pi) pi*sin(x) sage: integral(sin(x), (x, pi, 2*pi)) -2 sage: integral(sin(x), (y, pi, 2*pi)) pi*sin(x)
sage: var('x, n') (x, n) sage: integral(x^n,x) Traceback (most recent call last): ... ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(n>0)', see `assume?` for more details) Is n equal to -1? sage: assume(n > 0) sage: integral(x^n,x) x^(n + 1)/(n + 1) sage: forget()
