Integral of (1)/(x*sqrt(x-11)) dx
The solution
The answer (Indefinite)
[src]
// / ____\ \
|| ____ |\/ 11 | |
||2*I*\/ 11 *acosh|------| |
|| | ___ | |
/ || \\/ x / 11 |
| ||------------------------ for --- > 1|
| 1 || 11 |x| |
| ------------ dx = C + |< |
| ________ || / ____\ |
| x*\/ x - 11 || ____ |\/ 11 | |
| || -2*\/ 11 *asin|------| |
/ || | ___ | |
|| \\/ x / |
|| ---------------------- otherwise |
\\ 11 /
∫xx−111dx=C+⎩⎨⎧11211iacosh(x11)−11211asin(x11)for∣x∣11>1otherwise
The graph
____ / ____\
2*I*\/ 11 *acosh\\/ 11 /
-oo*I + ------------------------
11
−∞i+11211iacosh(11)
=
____ / ____\
2*I*\/ 11 *acosh\\/ 11 /
-oo*I + ------------------------
11
−∞i+11211iacosh(11)
-oo*i + 2*i*sqrt(11)*acosh(sqrt(11))/11
(0.0 - 13.3079670796836j)
(0.0 - 13.3079670796836j)
Use the examples entering the upper and lower limits of integration.