1 / | | x | ------------ dx | 2 | x + 3*x + 4 | / 0
Integral(x/(x^2 + 3*x + 4), (x, 0, 1))
/ | | x | 1*------------ dx | 2 | x + 3*x + 4 | /
/ 1*2*x + 3 \ |--------------| / -3 \ | 2 | |-----| x \1*x + 3*x + 4/ \2*7/4/ ------------ = ---------------- + --------------------------- 2 2 2 x + 3*x + 4 / ___ ___\ |-2*\/ 7 3*\/ 7 | |--------*x - -------| + 1 \ 7 7 /
/ | | x | 1*------------ dx | 2 = | x + 3*x + 4 | /
/ | | 1 / 6* | --------------------------- dx | | 2 | 1*2*x + 3 | / ___ ___\ | -------------- dx | |-2*\/ 7 3*\/ 7 | | 2 | |--------*x - -------| + 1 | 1*x + 3*x + 4 | \ 7 7 / | | / / -------------------- - ----------------------------------- 2 7
/ | | 1*2*x + 3 | -------------- dx | 2 | 1*x + 3*x + 4 | / -------------------- 2
2 u = x + 3*x
/ | | 1 | ----- du | 4 + u | / log(4 + u) ----------- = ---------- 2 2
/ | | 1*2*x + 3 | -------------- dx | 2 | 1*x + 3*x + 4 | / 2 \ / log\4 + x + 3*x/ -------------------- = ----------------- 2 2
/ | | 1 -6* | --------------------------- dx | 2 | / ___ ___\ | |-2*\/ 7 3*\/ 7 | | |--------*x - -------| + 1 | \ 7 7 / | / ------------------------------------ 7
___ ___ 3*\/ 7 2*x*\/ 7 v = - ------- - --------- 7 7
/ | | 1 -6* | ------ dv | 2 | 1 + v | / -6*atan(v) --------------- = ---------- 7 7
/ | | 1 -6* | --------------------------- dx | 2 | / ___ ___\ | |-2*\/ 7 3*\/ 7 | | |--------*x - -------| + 1 / ___ ___\ | \ 7 7 / ___ |3*\/ 7 2*x*\/ 7 | | -3*\/ 7 *atan|------- + ---------| / \ 7 7 / ------------------------------------ = ---------------------------------- 7 7
/ ___ ___\ ___ |3*\/ 7 2*x*\/ 7 | / 2 \ 3*\/ 7 *atan|------- + ---------| log\4 + x + 3*x/ \ 7 7 / C + ----------------- - --------------------------------- 2 7
/ ___ \ / ___ |2*\/ 7 *(3/2 + x)| | / 2 \ 3*\/ 7 *atan|-----------------| | x log\4 + x + 3*x/ \ 7 / | ------------ dx = C + ----------------- - ------------------------------- | 2 2 7 | x + 3*x + 4 | /
/ ___\ / ___\ ___ |5*\/ 7 | ___ |3*\/ 7 | 3*\/ 7 *atan|-------| 3*\/ 7 *atan|-------| log(8) log(4) \ 7 / \ 7 / ------ - ------ - --------------------- + --------------------- 2 2 7 7
=
/ ___\ / ___\ ___ |5*\/ 7 | ___ |3*\/ 7 | 3*\/ 7 *atan|-------| 3*\/ 7 *atan|-------| log(8) log(4) \ 7 / \ 7 / ------ - ------ - --------------------- + --------------------- 2 2 7 7
Use the examples entering the upper and lower limits of integration.