Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of (2x+3)
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Integral of 1-7*x^2
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Integral of (x+2)/(x(x-3))
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Integral of x/(2*x+1)
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Identical expressions
- sqrt(one + one /(four (x- one)))
- square root of (1 plus 1 divide by (4(x minus 1)))
- square root of (one plus one divide by (four (x minus one)))
- √(1+1/(4(x-1)))
- sqrt1+1/4x-1
- sqrt(1+1 divide by (4(x-1)))
- sqrt(1+1/(4(x-1)))dx
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Similar expressions
- sqrt(1+1/(4(x+1)))
- sqrt(1-1/(4(x-1)))
Integral of sqrt(1+1/(4(x-1))) dx
The solution
You have entered
[src]
2 / | | _______________ | / 1 | / 1 + --------- dx | \/ 4*(x - 1) | / 1
$$\int\limits_{1}^{2} \sqrt{1 + \frac{1}{4 \left(x - 1\right)}}\, dx$$
Integral(sqrt(1 + 1/(4*(x - 1))), (x, 1, 2))
The answer (Indefinite)
[src]
/ | | _______________ / ________\ ________ __________ | / 1 asinh\2*\/ -1 + x / \/ -1 + x *\/ -3 + 4*x | / 1 + --------- dx = C + ------------------- + ----------------------- | \/ 4*(x - 1) 4 2 | /
$$\int \sqrt{1 + \frac{1}{4 \left(x - 1\right)}}\, dx = C + \frac{\sqrt{x - 1} \sqrt{4 x - 3}}{2} + \frac{\operatorname{asinh}{\left(2 \sqrt{x - 1} \right)}}{4}$$
The graph
The answer
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___ \/ 5 asinh(2) ----- + -------- 2 4
$$\frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\sqrt{5}}{2}$$
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___ \/ 5 asinh(2) ----- + -------- 2 4
$$\frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\sqrt{5}}{2}$$
sqrt(5)/2 + asinh(2)/4
Use the examples entering the upper and lower limits of integration.