Arc Length in the Plane.

`Arc Length x-y` = Int((1+`f '`(x)^2)^(1/2),x = a .. b)

`Arc Length y-x` = Int((1+`g '`(y)^2)^(1/2),y = c .. d)

`Parametric Arc Length` = Int((`x '`(t)^2+` y'`(t)^2)^(1/2),t = t[1] .. t[2])

Arc Length Exercises 1.

`Arc Length Exercise 1.1:   `*y = 2/3*(x^2-1)^(3/2), x = 1 .. 3

`Arc Length Exercise 1.2:   `*y = 1/3*(x^2+2)^(3/2), x = 0 .. 1

`Arc Length Exercise 1.3:   `*y = ln(sec(x)), x = 0 .. 1/4*Pi

Integration by Parts.

Int(u,v) = u*v-Int(v,u)

Indefinite Integrals 1.

`Indefinite Integrals Exercise 1.1:   `*Int(x*sin(x),x)

`Indefinite Integrals Exercise 1.2:   `*Int(ln(x),x)

`Indefinite Integrals Exercise 1.3:   `*Int(x*exp(x),x)

`Indefinite Integrals Exercise 1.4:   `*Int(x^2*exp(x),x)

`Indefinite Integrals Exercise 1.5:   `*Int(x^3*exp(x),x)

`Indefinite Integrals Exercise 1.6:   `*Int(exp(x)*sin(x),x)

`Indefinite Integrals Exercise 1.7:   `*Int(sec(x),x)

`Indefinite Integrals Exercise 1.8:   `*Int(sec(x)^2,x)

`Indefinite Integrals Exercise 1.9:   `*Int(sec(x)^3,x)

`Indefinite Integrals Exercise 1.10:   `*Int(x^n*exp(a*x),x)