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- Improper integral
- Double Integral
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- Curvilinear integral
- Derivative Step by Step
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How to use it?
- Integral of d{x}:
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Integral of sin(5x)
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Integral of sqrt(1+x^2)/x
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Integral of t^2
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Integral of (x-1)^1/2
- Limit of the function:
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sqrt(1+x^2)/x
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Identical expressions
- sqrt(one +x^ two)/x
- square root of (1 plus x squared ) divide by x
- square root of (one plus x to the power of two) divide by x
- √(1+x^2)/x
- sqrt(1+x2)/x
- sqrt1+x2/x
- sqrt(1+x²)/x
- sqrt(1+x to the power of 2)/x
- sqrt1+x^2/x
- sqrt(1+x^2) divide by x
- sqrt(1+x^2)/xdx
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Similar expressions
- sqrt(1-x^2)/x
Integral of sqrt(1+x^2)/x dx
The solution
You have entered
[src]
1 / | | ________ | / 2 | \/ 1 + x | ----------- dx | x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x^{2} + 1}}{x}\, dx$$
Integral(sqrt(1 + x^2)/x, (x, 0, 1))
The answer (Indefinite)
[src]
/
|
| ________
| / 2
| \/ 1 + x /1\ x 1
| ----------- dx = C - asinh|-| + ------------- + ---------------
| x \x/ ________ ________
| / 1 / 1
/ / 1 + -- x* / 1 + --
/ 2 / 2
\/ x \/ x
$$\int \frac{\sqrt{x^{2} + 1}}{x}\, dx = C + \frac{x}{\sqrt{1 + \frac{1}{x^{2}}}} - \operatorname{asinh}{\left(\frac{1}{x} \right)} + \frac{1}{x \sqrt{1 + \frac{1}{x^{2}}}}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.