1 / | | 3*x + 4 | ------------- dx | 2 | x + 6*x + 13 | / 0
Integral((3*x + 4)/(x^2 + 6*x + 13), (x, 0, 1))
/ | | 3*x + 4 | ------------- dx | 2 | x + 6*x + 13 | /
2*x + 6 3*------------- /-5 \ 2 |---| 3*x + 4 x + 6*x + 13 \ 4 / ------------- = --------------- + -------------- 2 2 2 x + 6*x + 13 / x 3\ |- - - -| + 1 \ 2 2/
/ | | 3*x + 4 | ------------- dx | 2 = | x + 6*x + 13 | /
/ | | 1 / 5* | -------------- dx | | 2 | 2*x + 6 | / x 3\ 3* | ------------- dx | |- - - -| + 1 | 2 | \ 2 2/ | x + 6*x + 13 | | / / - ---------------------- + --------------------- 4 2
/ | | 2*x + 6 3* | ------------- dx | 2 | x + 6*x + 13 | / --------------------- 2
2 u = x + 6*x
/ | | 1 3* | ------ du | 13 + u | / 3*log(13 + u) -------------- = ------------- 2 2
/ | | 2*x + 6 3* | ------------- dx | 2 | x + 6*x + 13 | / 2 \ / 3*log\13 + x + 6*x/ --------------------- = -------------------- 2 2
/ | | 1 -5* | -------------- dx | 2 | / x 3\ | |- - - -| + 1 | \ 2 2/ | / ----------------------- 4
3 x v = - - - - 2 2
/ | | 1 -5* | ------ dv | 2 | 1 + v | / -5*atan(v) --------------- = ---------- 4 4
/ | | 1 -5* | -------------- dx | 2 | / x 3\ | |- - - -| + 1 | \ 2 2/ /3 x\ | -5*atan|- + -| / \2 2/ ----------------------- = -------------- 4 2
/3 x\ 5*atan|- + -| / 2 \ \2 2/ 3*log\13 + x + 6*x/ C - ------------- + -------------------- 2 2
/ /3 x\ | 5*atan|- + -| / 2 \ | 3*x + 4 \2 2/ 3*log\13 + x + 6*x/ | ------------- dx = C - ------------- + -------------------- | 2 2 2 | x + 6*x + 13 | /
5*atan(2) 3*log(13) 3*log(20) 5*atan(3/2) - --------- - --------- + --------- + ----------- 2 2 2 2
=
5*atan(2) 3*log(13) 3*log(20) 5*atan(3/2) - --------- - --------- + --------- + ----------- 2 2 2 2
-5*atan(2)/2 - 3*log(13)/2 + 3*log(20)/2 + 5*atan(3/2)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.