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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*e^(x*(-2))
- Integral of ((1-x)/(1+x))^(1/2)
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Integral of 1/6x
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Integral of x^3(e^x^2)
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Identical expressions
- sqrt(x^ two + four)/x
- square root of (x squared plus 4) divide by x
- square root of (x to the power of two plus four) divide by x
- √(x^2+4)/x
- sqrt(x2+4)/x
- sqrtx2+4/x
- sqrt(x²+4)/x
- sqrt(x to the power of 2+4)/x
- sqrtx^2+4/x
- sqrt(x^2+4) divide by x
- sqrt(x^2+4)/xdx
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Similar expressions
- sqrt(x^2-4)/x
Integral of sqrt(x^2+4)/x dx
The solution
You have entered
[src]
oo / | | ________ | / 2 | \/ x + 4 | ----------- dx | x | / 0
$$\int\limits_{0}^{\infty} \frac{\sqrt{x^{2} + 4}}{x}\, dx$$
Integral(sqrt(x^2 + 4)/x, (x, 0, oo))
The answer (Indefinite)
[src]
/
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| ________
| / 2
| \/ x + 4 /2\ x 4
| ----------- dx = C - 2*asinh|-| + ------------- + ---------------
| x \x/ ________ ________
| / 4 / 4
/ / 1 + -- x* / 1 + --
/ 2 / 2
\/ x \/ x
$$\int \frac{\sqrt{x^{2} + 4}}{x}\, dx = C + \frac{x}{\sqrt{1 + \frac{4}{x^{2}}}} - 2 \operatorname{asinh}{\left(\frac{2}{x} \right)} + \frac{4}{x \sqrt{1 + \frac{4}{x^{2}}}}$$
The graph
Use the examples entering the upper and lower limits of integration.