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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of e^(-x)
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Integral of -sin(x)
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Integral of cos(x/2)
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Integral of x-2
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Identical expressions
- d×x/(2x-sqrt2x)
- d×x divide by (2x minus square root of 2x)
- d×x/(2x-√2x)
- d×x/2x-sqrt2x
- d×x divide by (2x-sqrt2x)
- d×x/(2x-sqrt2x)dx
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Similar expressions
- d×x/(2x+sqrt2x)
Integral of d×x/(2x-sqrt2x) dx
The solution
You have entered
[src]
2 / | | d*x | ------------- dx | _____ | 2*x - \/ 2*x | / 1/2
$$\int\limits_{\frac{1}{2}}^{2} \frac{d x}{2 x - \sqrt{2 x}}\, dx$$
Integral((d*x)/(2*x - sqrt(2*x)), (x, 1/2, 2))
The answer (Indefinite)
[src]
/ | / ___ ___\ ___ ___ | d*x d*x d*log\- \/ 2 + 2*\/ x / d*\/ 2 *\/ x | ------------- dx = C + --- + ------------------------ + ------------- | _____ 2 2 2 | 2*x - \/ 2*x | /
$$\int \frac{d x}{2 x - \sqrt{2 x}}\, dx = C + \frac{\sqrt{2} d \sqrt{x}}{2} + \frac{d x}{2} + \frac{d \log{\left(2 \sqrt{x} - \sqrt{2} \right)}}{2}$$
The answer
[src]
/ / ___\\
| log\\/ 2 /|
oo*sign(d) + d*|2 + ----------|
\ 2 /
$$d \left(\frac{\log{\left(\sqrt{2} \right)}}{2} + 2\right) + \infty \operatorname{sign}{\left(d \right)}$$
=
=
/ / ___\\
| log\\/ 2 /|
oo*sign(d) + d*|2 + ----------|
\ 2 /
$$d \left(\frac{\log{\left(\sqrt{2} \right)}}{2} + 2\right) + \infty \operatorname{sign}{\left(d \right)}$$
oo*sign(d) + d*(2 + log(sqrt(2))/2)
Use the examples entering the upper and lower limits of integration.