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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+x)/x
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Integral of e^3
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Integral of x^3*exp(x^2)
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Integral of (x+1)^4
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Identical expressions
- one /(xsqrt(x- one))
- 1 divide by (x square root of (x minus 1))
- one divide by (x square root of (x minus one))
- 1/(x√(x-1))
- 1/xsqrtx-1
- 1 divide by (xsqrt(x-1))
- 1/(xsqrt(x-1))dx
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Similar expressions
- 1/(x*sqrt(x-1))dx
- 1/xsqrt(x-1)
- 1/(xsqrt(x-16))
- (1)/(x*sqrt(x-11))
- 1/(x*sqrt(x-1))
- 1/(xsqrt(x+1))
Integral of 1/(xsqrt(x-1)) dx
The solution
You have entered
[src]
1 / | | 1 | ----------- dx | _______ | x*\/ x - 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{x - 1}}\, dx$$
Integral(1/(x*sqrt(x - 1)), (x, 0, 1))
The answer (Indefinite)
[src]
// / 1 \ 1 \ / ||2*I*acosh|-----| for --- > 1| | || | ___| |x| | | 1 || \\/ x / | | ----------- dx = C + |< | | _______ || / 1 \ | | x*\/ x - 1 || -2*asin|-----| otherwise | | || | ___| | / \\ \\/ x / /
$$\int \frac{1}{x \sqrt{x - 1}}\, dx = C + \begin{cases} 2 i \operatorname{acosh}{\left(\frac{1}{\sqrt{x}} \right)} & \text{for}\: \frac{1}{\left|{x}\right|} > 1 \\- 2 \operatorname{asin}{\left(\frac{1}{\sqrt{x}} \right)} & \text{otherwise} \end{cases}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.