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