1 / | | 1 | ------------- dx | 2 | x + 2*x + 10 | / 0
Integral(1/(x^2 + 2*x + 10), (x, 0, 1))
/ | | 1 | ------------- dx | 2 | x + 2*x + 10 | /
1 1 ------------- = ------------------ 2 / 2 \ x + 2*x + 10 |/ x 1\ | 9*||- - - -| + 1| \\ 3 3/ /
/ | | 1 | ------------- dx | 2 = | x + 2*x + 10 | /
/ | | 1 | -------------- dx | 2 | / x 1\ | |- - - -| + 1 | \ 3 3/ | / -------------------- 9
/ | | 1 | -------------- dx | 2 | / x 1\ | |- - - -| + 1 | \ 3 3/ | / -------------------- 9
1 x v = - - - - 3 3
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 9 9
/ | | 1 | -------------- dx | 2 | / x 1\ | |- - - -| + 1 | \ 3 3/ /1 x\ | atan|- + -| / \3 3/ -------------------- = ----------- 9 3
/1 x\ atan|- + -| \3 3/ C + ----------- 3
/ /1 x\ | atan|- + -| | 1 \3 3/ | ------------- dx = C + ----------- | 2 3 | x + 2*x + 10 | /
atan(1/3) atan(2/3) - --------- + --------- 3 3
=
atan(1/3) atan(2/3) - --------- + --------- 3 3
-atan(1/3)/3 + atan(2/3)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.