Integrals
Indefinite Integrals
compute an indefinite integral
int x^5 dx
integrate x^2 sin^3 x dx
int e^t sin(5t) dt
compute an indefinite integral that cannot be expressed in elementary terms
int e^(-t^2) dt
integrate 1/sqrt(1-u^4)
Definite Integrals
compute a definite integral
integrate sin x dx from x=0 to pi
int e^(-a t) dt, t=0..a
compute an improper integral
int sinx/x dx, x=0..infinity
int e^(-t^2) dt, t=-infinity to infinity
Multiple Integrals
compute a multiple integral
integrate x^2 sin y dx dy, x=0..1, y=0..pi
int (x^2 y^2 + x y^3) dx dy, x=-2 to 2, y=-2 to 2
int sin^2 x + y sin z dx dy dz , x=0..pi, y=0..1, z=0..pi
compute an integral over an unbounded region
int e^-(x^2+y^2) dx dy, x=-oo to oo, y=-oo to oo
Numerical Integration
numerically integrate functions that cannot be integrated symbolically
integrate sin(cos x) from x=0 to 1
integrate sqrt( (1+x^2)/(1+x^4) ) dx, x=0..1
Integral Representations
find integral representations for a function
log x integral representation
gamma(x) integral representation
Fresnel S(x) integral rep