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