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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^2-x+1)/(x^2+x+1)^2
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Integral of x/(1+sqrt(x))
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Integral of x/(1+3*x^2)
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Integral of tan^3xdx
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Identical expressions
- one /(x(x+ two)^(one / two))
- 1 divide by (x(x plus 2) to the power of (1 divide by 2))
- one divide by (x(x plus two) to the power of (one divide by two))
- 1/(x(x+2)(1/2))
- 1/xx+21/2
- 1/xx+2^1/2
- 1 divide by (x(x+2)^(1 divide by 2))
- 1/(x(x+2)^(1/2))dx
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Similar expressions
- 1/(x(x-2)^(1/2))
Integral of 1/(x(x+2)^(1/2)) dx
The solution
You have entered
[src]
-1 / | | 1 | ----------- dx | _______ | x*\/ x + 2 | / -2
$$\int\limits_{-2}^{-1} \frac{1}{x \sqrt{x + 2}}\, dx$$
Integral(1/(x*sqrt(x + 2)), (x, -2, -1))
The answer (Indefinite)
[src]
// / ___ _______\ \ / || ___ |\/ 2 *\/ 2 + x | |2 + x| | | ||-\/ 2 *acoth|---------------| for ------- > 1| | 1 || \ 2 / 2 | | ----------- dx = C + |< | | _______ || / ___ _______\ | | x*\/ x + 2 || ___ |\/ 2 *\/ 2 + x | | | ||-\/ 2 *atanh|---------------| otherwise | / \\ \ 2 / /
$$\int \frac{1}{x \sqrt{x + 2}}\, dx = C + \begin{cases} - \sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \sqrt{x + 2}}{2} \right)} & \text{for}\: \frac{\left|{x + 2}\right|}{2} > 1 \\- \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \sqrt{x + 2}}{2} \right)} & \text{otherwise} \end{cases}$$
The graph
The answer
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/ ___\
___ |\/ 2 |
-\/ 2 *atanh|-----|
\ 2 /
$$- \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2}}{2} \right)}$$
=
=
/ ___\
___ |\/ 2 |
-\/ 2 *atanh|-----|
\ 2 /
$$- \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2}}{2} \right)}$$
-sqrt(2)*atanh(sqrt(2)/2)
Use the examples entering the upper and lower limits of integration.