1 / | | 5*x - 2 | ------- dx | 2 | x + 9 | / 0
Integral((5*x - 2)/(x^2 + 9), (x, 0, 1))
/ | | 5*x - 2 | ------- dx | 2 | x + 9 | /
2*x 5*------------ /-2 \ 2 |---| 5*x - 2 x + 0*x + 9 \ 9 / ------- = -------------- + ---------- 2 2 2 x + 9 /-x \ |---| + 1 \ 3 /
/ | | 5*x - 2 | ------- dx | 2 = | x + 9 | /
/ | | 1 / 2* | ---------- dx | | 2 | 2*x | /-x \ 5* | ------------ dx | |---| + 1 | 2 | \ 3 / | x + 0*x + 9 | | / / - ------------------ + -------------------- 9 2
/ | | 2*x 5* | ------------ dx | 2 | x + 0*x + 9 | / -------------------- 2
2 u = x
/ | | 1 5* | ----- du | 9 + u | / 5*log(9 + u) ------------- = ------------ 2 2
/ | | 2*x 5* | ------------ dx | 2 | x + 0*x + 9 | / 2\ / 5*log\9 + x / -------------------- = ------------- 2 2
/ | | 1 -2* | ---------- dx | 2 | /-x \ | |---| + 1 | \ 3 / | / ------------------- 9
-x v = --- 3
/ | | 1 -2* | ------ dv | 2 | 1 + v | / -2*atan(v) --------------- = ---------- 9 9
/ | | 1 -2* | ---------- dx | 2 | /-x \ | |---| + 1 | \ 3 / /x\ | -2*atan|-| / \3/ ------------------- = ---------- 9 3
/x\ 2*atan|-| / 2\ \3/ 5*log\9 + x / C - --------- + ------------- 3 2
/ /x\ | 2*atan|-| / 2\ | 5*x - 2 \3/ 5*log\9 + x / | ------- dx = C - --------- + ------------- | 2 3 2 | x + 9 | /
5*log(9) 2*atan(1/3) 5*log(10) - -------- - ----------- + --------- 2 3 2
=
5*log(9) 2*atan(1/3) 5*log(10) - -------- - ----------- + --------- 2 3 2
-5*log(9)/2 - 2*atan(1/3)/3 + 5*log(10)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.