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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x/sqrt(-x^2+10x+11)-(-5)/sqrt(-x^2+10x+11)
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Integral of sin^4(x)*cos^6(x)
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Integral of ∫sin²xcos²xdx
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Integral of 8x^3
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Identical expressions
- x/sqrt(-x^ two +10x+ eleven)-(- five)/sqrt(-x^ two +10x+ eleven)
- x divide by square root of ( minus x squared plus 10x plus 11) minus ( minus 5) divide by square root of ( minus x squared plus 10x plus 11)
- x divide by square root of ( minus x to the power of two plus 10x plus eleven) minus ( minus five) divide by square root of ( minus x to the power of two plus 10x plus eleven)
- x/√(-x^2+10x+11)-(-5)/√(-x^2+10x+11)
- x/sqrt(-x2+10x+11)-(-5)/sqrt(-x2+10x+11)
- x/sqrt-x2+10x+11--5/sqrt-x2+10x+11
- x/sqrt(-x²+10x+11)-(-5)/sqrt(-x²+10x+11)
- x/sqrt(-x to the power of 2+10x+11)-(-5)/sqrt(-x to the power of 2+10x+11)
- x/sqrt-x^2+10x+11--5/sqrt-x^2+10x+11
- x divide by sqrt(-x^2+10x+11)-(-5) divide by sqrt(-x^2+10x+11)
- x/sqrt(-x^2+10x+11)-(-5)/sqrt(-x^2+10x+11)dx
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Similar expressions
- x/sqrt(-x^2-10x+11)-(-5)/sqrt(-x^2+10x+11)
- x/sqrt(x^2+10x+11)-(-5)/sqrt(-x^2+10x+11)
- x/sqrt(-x^2+10x+11)-(-5)/sqrt(x^2+10x+11)
- x/sqrt(-x^2+10x+11)-(-5)/sqrt(-x^2-10x+11)
- x/sqrt(-x^2+10x+11)-(5)/sqrt(-x^2+10x+11)
- x/sqrt(-x^2+10x+11)+(-5)/sqrt(-x^2+10x+11)
- x/sqrt(-x^2+10x-11)-(-5)/sqrt(-x^2+10x+11)
- x/sqrt(-x^2+10x+11)-(-5)/sqrt(-x^2+10x-11)
Integral of x/sqrt(-x^2+10x+11)-(-5)/sqrt(-x^2+10x+11) dx
The solution
You have entered
[src]
4 / | | / x -5 \ | |--------------------- - ---------------------| dx | | __________________ __________________| | | / 2 / 2 | | \\/ - x + 10*x + 11 \/ - x + 10*x + 11 / | / 2
$$\int\limits_{2}^{4} \left(\frac{x}{\sqrt{- x^{2} + 10 x + 11}} - - \frac{5}{\sqrt{- x^{2} + 10 x + 11}}\right)\, dx$$
The answer (Indefinite)
[src]
/ / | ________________ | | / x -5 \ / 2 | 1 / 5 x\ | |--------------------- - ---------------------| dx = C - \/ 11 - x + 10*x + 5* | --------------------- dx + 5*asin|- - + -| | | __________________ __________________| | __________________ \ 6 6/ | | / 2 / 2 | | / 2 | \\/ - x + 10*x + 11 \/ - x + 10*x + 11 / | \/ - x + 10*x + 11 | | / /
$$-\sqrt{-x^2+10\,x+11}-10\,\arcsin \left({{10-2\,x}\over{12}}\right)$$
The graph
The answer
[src]
____ ___ 5*pi
- \/ 35 - 10*asin(1/6) + 3*\/ 3 + ----
3
$$-{{30\,\arcsin \left({{1}\over{6}}\right)-5\,\pi+3\,\sqrt{35}-3^{{{
5}\over{2}}}}\over{3}}$$
=
=
____ ___ 5*pi
- \/ 35 - 10*asin(1/6) + 3*\/ 3 + ----
3
$$- \sqrt{35} - 10 \operatorname{asin}{\left(\frac{1}{6} \right)} + 3 \sqrt{3} + \frac{5 \pi}{3}$$
The graph
Use the examples entering the upper and lower limits of integration.