Substitusjon 

 

Substitusjon 

> restart:
 

> A:=Int(x^2*sin(x^3+4),x):
 

> Substitusjon(A,u=x^3+4);
 

 

 

Int(`*`(`^`(x, 2), `*`(sin(`+`(`*`(`^`(x, 3)), 4)))), x) = Int(`+`(`*`(`/`(1, 3), `*`(sin(u)))), u)
Int(`+`(`*`(`/`(1, 3), `*`(sin(u)))), u) = `+`(`-`(`*`(`/`(1, 3), `*`(cos(u)))), C)
Int(`+`(`*`(`/`(1, 3), `*`(sin(u)))), u) = `+`(`-`(`*`(`/`(1, 3), `*`(cos(`+`(`*`(`^`(x, 3)), 4))))), C)
 

> A:=Int(x/sqrt(5+2*x^2),x=0..1):
 

> Substitusjon(A,u=5+2*x^2);
 

 

 

Int(`/`(`*`(x), `*`(`^`(`+`(5, `*`(2, `*`(`^`(x, 2)))), `/`(1, 2)))), x = 0 .. 1) = Int(`+`(`/`(`*`(`/`(1, 4)), `*`(`^`(u, `/`(1, 2))))), u = 5 .. 7)
Int(`+`(`/`(`*`(`/`(1, 4)), `*`(`^`(u, `/`(1, 2))))), u = 5 .. 7) = `+`(`*`(`/`(1, 10), `*`(`^`(5, `/`(1, 2)), `*`(`+`(`-`(5), `*`(`^`(7, `/`(1, 2)), `*`(`^`(5, `/`(1, 2)))))))))
Int(`+`(`/`(`*`(`/`(1, 4)), `*`(`^`(u, `/`(1, 2))))), u = 5 .. 7) = .2048416665