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