1 / | | 1 | -------------- dx | 2 | x + 10*x + 29 | / 0
Integral(1/(x^2 + 10*x + 29), (x, 0, 1))
/ | | 1 | -------------- dx | 2 | x + 10*x + 29 | /
1 1 -------------- = ------------------ 2 / 2 \ x + 10*x + 29 |/ x 5\ | 4*||- - - -| + 1| \\ 2 2/ /
/ | | 1 | -------------- dx | 2 = | x + 10*x + 29 | /
/ | | 1 | -------------- dx | 2 | / x 5\ | |- - - -| + 1 | \ 2 2/ | / -------------------- 4
/ | | 1 | -------------- dx | 2 | / x 5\ | |- - - -| + 1 | \ 2 2/ | / -------------------- 4
5 x v = - - - - 2 2
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 4 4
/ | | 1 | -------------- dx | 2 | / x 5\ | |- - - -| + 1 | \ 2 2/ /5 x\ | atan|- + -| / \2 2/ -------------------- = ----------- 4 2
/5 x\ atan|- + -| \2 2/ C + ----------- 2
/ /5 x\ | atan|- + -| | 1 \2 2/ | -------------- dx = C + ----------- | 2 2 | x + 10*x + 29 | /
atan(3) atan(5/2) ------- - --------- 2 2
=
atan(3) atan(5/2) ------- - --------- 2 2
atan(3)/2 - atan(5/2)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.