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- Improper integral
- Double Integral
- Triple Integral
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How to use it?
- Integral of d{x}:
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Integral of x^4/(1+x^2)
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Integral of x^5/(x^2+1)
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Integral of x^2/(√(1-x^2))
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Integral of (tan(x))^2/(cos(x))^2
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Identical expressions
- sqrt(x)/(x- two)
- square root of (x) divide by (x minus 2)
- square root of (x) divide by (x minus two)
- √(x)/(x-2)
- sqrtx/x-2
- sqrt(x) divide by (x-2)
- sqrt(x)/(x-2)dx
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Similar expressions
- sqrt(x)/(x+2)
- ((3sqrt(x))/x-(2-x^3)+1)dx
Integral of sqrt(x)/(x-2) dx
The solution
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[src]
6 / | | ___ | \/ x | ----- dx | x - 2 | / 2
$$\int\limits_{2}^{6} \frac{\sqrt{x}}{x - 2}\, dx$$
Integral(sqrt(x)/(x - 2), (x, 2, 6))
The answer (Indefinite)
[src]
// / ___ ___\ \
|| ___ |\/ 2 *\/ x | |
/ ||-\/ 2 *acoth|-----------| |
| || \ 2 / |
| ___ ||-------------------------- for x > 2|
| \/ x ___ || 2 |
| ----- dx = C + 2*\/ x + 4*|< |
| x - 2 || / ___ ___\ |
| || ___ |\/ 2 *\/ x | |
/ ||-\/ 2 *atanh|-----------| |
|| \ 2 / |
||-------------------------- for x < 2|
\\ 2 /
$$\int \frac{\sqrt{x}}{x - 2}\, dx = C + 2 \sqrt{x} + 4 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \sqrt{x}}{2} \right)}}{2} & \text{for}\: x > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \sqrt{x}}{2} \right)}}{2} & \text{for}\: x < 2 \end{cases}\right)$$
The graph
Use the examples entering the upper and lower limits of integration.