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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 (x)/(1+x^2)
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Integral of dx/(5-3*x)
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Integral of dx/(5-2*x)
- Derivative of:
- sqrt(x)/(x^2+1)
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Identical expressions
- sqrt(x)/(x^ two + one)
- square root of (x) divide by (x squared plus 1)
- square root of (x) divide by (x to the power of two plus one)
- √(x)/(x^2+1)
- sqrt(x)/(x2+1)
- sqrtx/x2+1
- sqrt(x)/(x²+1)
- sqrt(x)/(x to the power of 2+1)
- sqrtx/x^2+1
- sqrt(x) divide by (x^2+1)
- sqrt(x)/(x^2+1)dx
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Similar expressions
- sqrt(x)/(x^2-1)
Integral of sqrt(x)/(x^2+1) dx
The solution
You have entered
[src]
1 / | | ___ | \/ x | ------ dx | 2 | x + 1 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x}}{x^{2} + 1}\, dx$$
Integral(sqrt(x)/(x^2 + 1), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | ___ ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ | \/ x \/ 2 *atan\1 + \/ 2 *\/ x / \/ 2 *atan\-1 + \/ 2 *\/ x / \/ 2 *log\1 + x + \/ 2 *\/ x / \/ 2 *log\1 + x - \/ 2 *\/ x / | ------ dx = C + --------------------------- + ---------------------------- - ------------------------------ + ------------------------------ | 2 2 2 4 4 | x + 1 | /
$$\int \frac{\sqrt{x}}{x^{2} + 1}\, dx = C + \frac{\sqrt{2} \log{\left(- \sqrt{2} \sqrt{x} + x + 1 \right)}}{4} - \frac{\sqrt{2} \log{\left(\sqrt{2} \sqrt{x} + x + 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2}$$
The graph
The answer
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___ / ___\ ___ ___ / ___\
\/ 2 *log\8 + 4*\/ 2 / pi*\/ 2 \/ 2 *log\8 - 4*\/ 2 /
- ---------------------- + -------- + ----------------------
4 4 4
$$- \frac{\sqrt{2} \log{\left(4 \sqrt{2} + 8 \right)}}{4} + \frac{\sqrt{2} \log{\left(8 - 4 \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \pi}{4}$$
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___ / ___\ ___ ___ / ___\
\/ 2 *log\8 + 4*\/ 2 / pi*\/ 2 \/ 2 *log\8 - 4*\/ 2 /
- ---------------------- + -------- + ----------------------
4 4 4
$$- \frac{\sqrt{2} \log{\left(4 \sqrt{2} + 8 \right)}}{4} + \frac{\sqrt{2} \log{\left(8 - 4 \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \pi}{4}$$
-sqrt(2)*log(8 + 4*sqrt(2))/4 + pi*sqrt(2)/4 + sqrt(2)*log(8 - 4*sqrt(2))/4
The graph
Use the examples entering the upper and lower limits of integration.