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- Integral of d{x}:
- Integral of x*y
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Integral of sqrt(1+e^(2*x))
- Integral of dx/(2sinx+5cosx)
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Integral of log^2x/x
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Identical expressions
- one /sqrt(x^ two +y^ two + one)
- 1 divide by square root of (x squared plus y squared plus 1)
- one divide by square root of (x to the power of two plus y to the power of two plus one)
- 1/√(x^2+y^2+1)
- 1/sqrt(x2+y2+1)
- 1/sqrtx2+y2+1
- 1/sqrt(x²+y²+1)
- 1/sqrt(x to the power of 2+y to the power of 2+1)
- 1/sqrtx^2+y^2+1
- 1 divide by sqrt(x^2+y^2+1)
- 1/sqrt(x^2+y^2+1)dx
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Similar expressions
- 1/sqrt(x^2-y^2+1)
- 1/sqrt(x^2+y^2-1)
Integral of 1/sqrt(x^2+y^2+1) dy
The solution
You have entered
[src]
1 / | | 1 | ---------------- dy | _____________ | / 2 2 | \/ x + y + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{\left(x^{2} + y^{2}\right) + 1}}\, dy$$
Integral(1/(sqrt(x^2 + y^2 + 1)), (y, 0, 1))
The answer (Indefinite)
[src]
/ | | 1 / y \ | ---------------- dy = C + asinh|-----------------------| | _____________ | ____________________| | / 2 2 | / / 2\ | | \/ x + y + 1 \\/ polar_lift\1 + x / / | /
$$\int \frac{1}{\sqrt{\left(x^{2} + y^{2}\right) + 1}}\, dy = C + \operatorname{asinh}{\left(\frac{y}{\sqrt{\operatorname{polar\_lift}{\left(x^{2} + 1 \right)}}} \right)}$$
The answer
[src]
/ 1 \
asinh|-----------------------|
| ____________________|
| / / 2\ |
\\/ polar_lift\1 + x / /
$$\operatorname{asinh}{\left(\frac{1}{\sqrt{\operatorname{polar\_lift}{\left(x^{2} + 1 \right)}}} \right)}$$
=
=
/ 1 \
asinh|-----------------------|
| ____________________|
| / / 2\ |
\\/ polar_lift\1 + x / /
$$\operatorname{asinh}{\left(\frac{1}{\sqrt{\operatorname{polar\_lift}{\left(x^{2} + 1 \right)}}} \right)}$$
asinh(1/sqrt(polar_lift(1 + x^2)))
Use the examples entering the upper and lower limits of integration.