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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (1+4x^2)^(1/2)
- Integral of x/(x^3-3x+2)
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Integral of √(9-x^2)
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Integral of (2x-4)
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Identical expressions
- one /x(x- one)^(- one / two)
- 1 divide by x(x minus 1) to the power of ( minus 1 divide by 2)
- one divide by x(x minus one) to the power of ( minus one divide by two)
- 1/x(x-1)(-1/2)
- 1/xx-1-1/2
- 1/xx-1^-1/2
- 1 divide by x(x-1)^(-1 divide by 2)
- 1/x(x-1)^(-1/2)dx
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Similar expressions
- 1/x(x+1)^(-1/2)
- 1/x(x-1)^(1/2)
Integral of 1/x(x-1)^(-1/2) dx
The solution
You have entered
[src]
oo / | | 1 | ----------- dx | _______ | x*\/ x - 1 | / 1
$$\int\limits_{1}^{\infty} \frac{1}{x \sqrt{x - 1}}\, dx$$
Integral(1/(x*sqrt(x - 1)), (x, 1, oo))
The answer (Indefinite)
[src]
/ | | 1 / 1 \ | ----------- dx = C - 2*atan|---------| | _______ | _______| | x*\/ x - 1 \\/ x - 1 / | /
$$\int \frac{1}{x \sqrt{x - 1}}\, dx = C - 2 \operatorname{atan}{\left(\frac{1}{\sqrt{x - 1}} \right)}$$
The graph
Use the examples entering the upper and lower limits of integration.