Integral of 1/(x*sqrt(2x-9)) dx
The solution
The answer (Indefinite)
[src]
// / ___\ \
|| |3*\/ 2 | |
||2*I*acosh|-------| |
|| | ___| |
/ || \2*\/ x / 9 |
| ||------------------ for ----- > 1|
| 1 || 3 2*|x| |
| ------------- dx = C + |< |
| _________ || / ___\ |
| x*\/ 2*x - 9 || |3*\/ 2 | |
| || -2*asin|-------| |
/ || | ___| |
|| \2*\/ x / |
|| ---------------- otherwise |
\\ 3 /
∫x2x−91dx=C+⎩⎨⎧32iacosh(2x32)−32asin(2x32)for2∣x∣9>1otherwise
The graph
/ ___\
|3*\/ 2 |
2*I*acosh|-------|
\ 2 /
-oo*I + ------------------
3
−∞i+32iacosh(232)
=
/ ___\
|3*\/ 2 |
2*I*acosh|-------|
\ 2 /
-oo*I + ------------------
3
−∞i+32iacosh(232)
-oo*i + 2*i*acosh(3*sqrt(2)/2)/3
(0.0 - 14.7373861695252j)
(0.0 - 14.7373861695252j)
Use the examples entering the upper and lower limits of integration.