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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
- Integral of 1/((x-1)*sqrt(x^2-1))
- Integral of 3*sinx*cosx
- Integral of dx/(3cosx-4sinx+5)
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Integral of cos^2(2x)
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Identical expressions
- one /((x- one)*sqrt(x^ two - one))
- 1 divide by ((x minus 1) multiply by square root of (x squared minus 1))
- one divide by ((x minus one) multiply by square root of (x to the power of two minus one))
- 1/((x-1)*√(x^2-1))
- 1/((x-1)*sqrt(x2-1))
- 1/x-1*sqrtx2-1
- 1/((x-1)*sqrt(x²-1))
- 1/((x-1)*sqrt(x to the power of 2-1))
- 1/((x-1)sqrt(x^2-1))
- 1/((x-1)sqrt(x2-1))
- 1/x-1sqrtx2-1
- 1/x-1sqrtx^2-1
- 1 divide by ((x-1)*sqrt(x^2-1))
- 1/((x-1)*sqrt(x^2-1))dx
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Similar expressions
- 1/((x+1)*sqrt(x^2-1))
- 1/((x-1)*sqrt(x^2+1))
Integral of 1/((x-1)*sqrt(x^2-1)) dx
The solution
You have entered
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1 / | | 1 | ------------------- dx | ________ | / 2 | (x - 1)*\/ x - 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x - 1\right) \sqrt{x^{2} - 1}}\, dx$$
Integral(1/((x - 1)*sqrt(x^2 - 1)), (x, 0, 1))
The answer (Indefinite)
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/ / | | | 1 | 1 | ------------------- dx = C + | ----------------------------- dx | ________ | __________________ | / 2 | \/ (1 + x)*(-1 + x) *(-1 + x) | (x - 1)*\/ x - 1 | | / /
$$\int \frac{1}{\left(x - 1\right) \sqrt{x^{2} - 1}}\, dx = C + \int \frac{1}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \left(x - 1\right)}\, dx$$
The answer
[src]
1 / | | 1 | --------------------- dx | _______ 3/2 | \/ 1 + x *(-1 + x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x - 1\right)^{\frac{3}{2}} \sqrt{x + 1}}\, dx$$
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1 / | | 1 | --------------------- dx | _______ 3/2 | \/ 1 + x *(-1 + x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x - 1\right)^{\frac{3}{2}} \sqrt{x + 1}}\, dx$$
Integral(1/(sqrt(1 + x)*(-1 + x)^(3/2)), (x, 0, 1))
Use the examples entering the upper and lower limits of integration.