1 / | | 1 | ------ dx | 2 | x + 3 | / 0
Integral(1/(x^2 + 3), (x, 0, 1))
/ | | 1 | ------ dx | 2 | x + 3 | /
1 1 ------ = -------------------- 2 / 2 \ x + 3 |/ ___ \ | ||-\/ 3 | | 3*||-------*x| + 1| \\ 3 / /
/ | | 1 | ------ dx | 2 = | x + 3 | /
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 3 | | |-------*x| + 1 | \ 3 / | / ---------------------- 3
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 3 | | |-------*x| + 1 | \ 3 / | / ---------------------- 3
___ -x*\/ 3 v = --------- 3
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 3 3
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 3 | | |-------*x| + 1 / ___\ | \ 3 / ___ |x*\/ 3 | | \/ 3 *atan|-------| / \ 3 / ---------------------- = ------------------- 3 3
/ ___\ ___ |x*\/ 3 | \/ 3 *atan|-------| \ 3 / C + ------------------- 3
/ ___\ / ___ |x*\/ 3 | | \/ 3 *atan|-------| | 1 \ 3 / | ------ dx = C + ------------------- | 2 3 | x + 3 | /
___ pi*\/ 3 -------- 18
=
___ pi*\/ 3 -------- 18
pi*sqrt(3)/18
Use the examples entering the upper and lower limits of integration.