1 / | | x | ---------- dx | 2 | 2 + x + x | / 0
Integral(x/(2 + x + x^2), (x, 0, 1))
/ | | x | ---------- dx | 2 | 2 + x + x | /
/ 2*x + 1 \ |----------| / -1 \ | 2 | |-----| x \x + x + 2/ \2*7/4/ ---------- = ------------ + ------------------------- 2 2 2 2 + x + x / ___ ___\ |-2*\/ 7 \/ 7 | |--------*x - -----| + 1 \ 7 7 /
/ | | x | ---------- dx | 2 = | 2 + x + x | /
/ | | 1 / 2* | ------------------------- dx | | 2 | 2*x + 1 | / ___ ___\ | ---------- dx | |-2*\/ 7 \/ 7 | | 2 | |--------*x - -----| + 1 | x + x + 2 | \ 7 7 / | | / / ---------------- - --------------------------------- 2 7
/ | | 2*x + 1 | ---------- dx | 2 | x + x + 2 | / ---------------- 2
2 u = x + x
/ | | 1 | ----- du | 2 + u | / log(2 + u) ----------- = ---------- 2 2
/ | | 2*x + 1 | ---------- dx | 2 | x + x + 2 | / 2\ / log\2 + x + x / ---------------- = --------------- 2 2
/ | | 1 -2* | ------------------------- dx | 2 | / ___ ___\ | |-2*\/ 7 \/ 7 | | |--------*x - -----| + 1 | \ 7 7 / | / ---------------------------------- 7
___ ___ \/ 7 2*x*\/ 7 v = - ----- - --------- 7 7
/ | | 1 -2* | ------ dv | 2 | 1 + v | / -2*atan(v) --------------- = ---------- 7 7
/ | | 1 -2* | ------------------------- dx | 2 | / ___ ___\ | |-2*\/ 7 \/ 7 | | |--------*x - -----| + 1 / ___ ___\ | \ 7 7 / ___ |\/ 7 2*x*\/ 7 | | -\/ 7 *atan|----- + ---------| / \ 7 7 / ---------------------------------- = ------------------------------- 7 7
/ ___ ___\ ___ |\/ 7 2*x*\/ 7 | / 2\ \/ 7 *atan|----- + ---------| log\2 + x + x / \ 7 7 / C + --------------- - ----------------------------- 2 7
/ ___ \ / ___ |2*\/ 7 *(1/2 + x)| | / 2\ \/ 7 *atan|-----------------| | x log\2 + x + x / \ 7 / | ---------- dx = C + --------------- - ----------------------------- | 2 2 7 | 2 + x + x | /
/ ___\ / ___\ ___ |3*\/ 7 | ___ |\/ 7 | \/ 7 *atan|-------| \/ 7 *atan|-----| log(4) log(2) \ 7 / \ 7 / ------ - ------ - ------------------- + ----------------- 2 2 7 7
=
/ ___\ / ___\ ___ |3*\/ 7 | ___ |\/ 7 | \/ 7 *atan|-------| \/ 7 *atan|-----| log(4) log(2) \ 7 / \ 7 / ------ - ------ - ------------------- + ----------------- 2 2 7 7
log(4)/2 - log(2)/2 - sqrt(7)*atan(3*sqrt(7)/7)/7 + sqrt(7)*atan(sqrt(7)/7)/7
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.