1 / | | 1 | ------------- dx | ________ | / 1 | / 2 - -- | / 2 | \/ x | / 0
Integral(1/(sqrt(2 - 1/x^2)), (x, 0, 1))
// ___________ \ || / 2 | / ||\/ -1 + 2*x | 2| | | ||-------------- for 2*|x | > 1| | 1 || 2 | | ------------- dx = C + |< | | ________ || __________ | | / 1 || / 2 | | / 2 - -- ||I*\/ 1 - 2*x | | / 2 ||--------------- otherwise | | \/ x \\ 2 / | /
1 / | | / x 2 | |-------------- for 2*x > 1 | | ___________ | | / 2 | |\/ -1 + 2*x | < dx | | -I*x | |------------- otherwise | | __________ | | / 2 | \\/ 1 - 2*x | / 0
=
1 / | | / x 2 | |-------------- for 2*x > 1 | | ___________ | | / 2 | |\/ -1 + 2*x | < dx | | -I*x | |------------- otherwise | | __________ | | / 2 | \\/ 1 - 2*x | / 0
Integral(Piecewise((x/sqrt(-1 + 2*x^2), 2*x^2 > 1), (-i*x/sqrt(1 - 2*x^2), True)), (x, 0, 1))
(0.505674648770025 - 0.454284972789841j)
(0.505674648770025 - 0.454284972789841j)
Use the examples entering the upper and lower limits of integration.