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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 x^4*e^x
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Integral of 1/(x^2+4x+8)
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Integral of y/sqrt(1+y^2)
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Integral of (1+cos^2x)/(1+cos2x)
- Canonical form:
- sqrt(x^2-9)
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Identical expressions
- sqrt(x^ two - nine)
- square root of (x squared minus 9)
- square root of (x to the power of two minus nine)
- √(x^2-9)
- sqrt(x2-9)
- sqrtx2-9
- sqrt(x²-9)
- sqrt(x to the power of 2-9)
- sqrtx^2-9
- sqrt(x^2-9)dx
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Similar expressions
- sqrt(x^2+9)
Integral of sqrt(x^2-9) dx
The solution
You have entered
[src]
3 / | | ________ | / 2 | \/ x - 9 dx | / 239 --- 100
$$\int\limits_{\frac{239}{100}}^{3} \sqrt{x^{2} - 9}\, dx$$
Integral(sqrt(x^2 - 1*9), (x, 239/100, 3))
Detail solution
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Add the constant of integration:
SqrtQuadraticRule(a=-9, b=0, c=1, context=sqrt(x**2 - 1*9), symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ | / _________\ _________ | ________ | / 2 | / 2 | / 2 9*log\2*x + 2*\/ -9 + x / x*\/ -9 + x | \/ x - 9 dx = C - --------------------------- + -------------- | 2 2 /
$${{x\,\sqrt{x^2-9}}\over{2}}-{{9\,\log \left(2\,\sqrt{x^2-9}+2\,x
\right)}\over{2}}$$
The graph
The answer
[src]
/ _____\
|239 7*I*\/ 671 |
9*log|--- + -----------| _____
9*log(3) \100 100 / 1673*I*\/ 671
- -------- + ------------------------ - --------------
2 2 20000
$${{9\,\log \left({{7\,\sqrt{671}\,i+239}\over{50}}\right)}\over{2}}-
{{9\,\log 6}\over{2}}-{{1673\,\sqrt{671}\,i}\over{20000}}$$
=
=
/ _____\
|239 7*I*\/ 671 |
9*log|--- + -----------| _____
9*log(3) \100 100 / 1673*I*\/ 671
- -------- + ------------------------ - --------------
2 2 20000
$$- \frac{9 \log{\left(3 \right)}}{2} - \frac{1673 \sqrt{671} i}{20000} + \frac{9 \log{\left(\frac{239}{100} + \frac{7 \sqrt{671} i}{100} \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.