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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x*x
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Integral of dx/(5-2*x)
- Integral of √xlogx
- Integral of 1/(x*sqrt(2x-9))
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Identical expressions
- one /(x*sqrt(2x- nine))
- 1 divide by (x multiply by square root of (2x minus 9))
- one divide by (x multiply by square root of (2x minus nine))
- 1/(x*√(2x-9))
- 1/(xsqrt(2x-9))
- 1/xsqrt2x-9
- 1 divide by (x*sqrt(2x-9))
- 1/(x*sqrt(2x-9))dx
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Similar expressions
- 1/x(sqrt2x-9)
- 1/(x*sqrt(2x+9))
- 1/(x*(sqrt(2)*(x))-9)
Integral of 1/(x*sqrt(2x-9)) dx
The solution
You have entered
[src]
1 / | | 1 | ------------- dx | _________ | x*\/ 2*x - 9 | / 0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{2 x - 9}}\, dx$$
Integral(1/(x*sqrt(2*x - 9)), (x, 0, 1))
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 /
$$\int \frac{1}{x \sqrt{2 x - 9}}\, dx = C + \begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{3 \sqrt{2}}{2 \sqrt{x}} \right)}}{3} & \text{for}\: \frac{9}{2 \left|{x}\right|} > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{3 \sqrt{2}}{2 \sqrt{x}} \right)}}{3} & \text{otherwise} \end{cases}$$
The graph
The answer
[src]
/ ___\
|3*\/ 2 |
2*I*acosh|-------|
\ 2 /
-oo*I + ------------------
3
$$- \infty i + \frac{2 i \operatorname{acosh}{\left(\frac{3 \sqrt{2}}{2} \right)}}{3}$$
=
=
/ ___\
|3*\/ 2 |
2*I*acosh|-------|
\ 2 /
-oo*I + ------------------
3
$$- \infty i + \frac{2 i \operatorname{acosh}{\left(\frac{3 \sqrt{2}}{2} \right)}}{3}$$
-oo*i + 2*i*acosh(3*sqrt(2)/2)/3
Use the examples entering the upper and lower limits of integration.