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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of y=x^2
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Integral of x^2*e^(-x)
- Integral of x^2*ln(x)
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Integral of x^2*e^x*dx
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Identical expressions
- sqrt(ten +x^ two)
- square root of (10 plus x squared )
- square root of (ten plus x to the power of two)
- √(10+x^2)
- sqrt(10+x2)
- sqrt10+x2
- sqrt(10+x²)
- sqrt(10+x to the power of 2)
- sqrt10+x^2
- sqrt(10+x^2)dx
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Similar expressions
- sqrt(10-x^2)
Integral of sqrt(10+x^2) dx
The solution
You have entered
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1 / | | _________ | / 2 | \/ 10 + x dx | / 0
$$\int\limits_{0}^{1} \sqrt{x^{2} + 10}\, dx$$
Integral(sqrt(10 + x^2), (x, 0, 1))
The answer (Indefinite)
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/ | _________ | _________ / ____\ / 2 | / 2 |x*\/ 10 | x*\/ 10 + x | \/ 10 + x dx = C + 5*asinh|--------| + -------------- | \ 10 / 2 /
$$\int \sqrt{x^{2} + 10}\, dx = C + \frac{x \sqrt{x^{2} + 10}}{2} + 5 \operatorname{asinh}{\left(\frac{\sqrt{10} x}{10} \right)}$$
The graph
The answer
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____ / ____\ \/ 11 |\/ 10 | ------ + 5*asinh|------| 2 \ 10 /
$$5 \operatorname{asinh}{\left(\frac{\sqrt{10}}{10} \right)} + \frac{\sqrt{11}}{2}$$
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____ / ____\ \/ 11 |\/ 10 | ------ + 5*asinh|------| 2 \ 10 /
$$5 \operatorname{asinh}{\left(\frac{\sqrt{10}}{10} \right)} + \frac{\sqrt{11}}{2}$$
sqrt(11)/2 + 5*asinh(sqrt(10)/10)
Use the examples entering the upper and lower limits of integration.