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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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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 tg²xdx
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Integral of sqrt(-8x-x^2)
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Integral of 6(2x-3)^2
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Identical expressions
- sqrt(-8x-x^ two)
- square root of ( minus 8x minus x squared )
- square root of ( minus 8x minus x to the power of two)
- √(-8x-x^2)
- sqrt(-8x-x2)
- sqrt-8x-x2
- sqrt(-8x-x²)
- sqrt(-8x-x to the power of 2)
- sqrt-8x-x^2
- sqrt(-8x-x^2)dx
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Similar expressions
- sqrt(-8x+x^2)
- sqrt(8x-x^2)
Integral of sqrt(-8x-x^2) dx
The solution
You have entered
[src]
0 / | | ___________ | / 2 | \/ -8*x - x dx | / -8
$$\int\limits_{-8}^{0} \sqrt{- x^{2} - 8 x}\, dx$$
Detail solution
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Now simplify:
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Add the constant of integration:
SqrtQuadraticRule(a=0, b=-8, c=-1, context=sqrt(-x**2 - 8*x), symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ | | ___________ ____________ | / 2 / x\ / 2 / x\ | \/ -8*x - x dx = C + 8*asin|1 + -| + \/ - x - 8*x *|2 + -| | \ 4/ \ 2/ /
$${{x\,\sqrt{-x^2-8\,x}}\over{2}}+2\,\sqrt{-x^2-8\,x}-8\,\arcsin
\left({{-2\,x-8}\over{8}}\right)$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.