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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^2*e^(x*(-2))
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Integral of e^(-x^3)
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Integral of -exp(-3*x)
- Integral of (xcosx)/(2+3x^3)
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Identical expressions
- sqrt((nine *x^ two - one)/x)
- square root of ((9 multiply by x squared minus 1) divide by x)
- square root of ((nine multiply by x to the power of two minus one) divide by x)
- √((9*x^2-1)/x)
- sqrt((9*x2-1)/x)
- sqrt9*x2-1/x
- sqrt((9*x²-1)/x)
- sqrt((9*x to the power of 2-1)/x)
- sqrt((9x^2-1)/x)
- sqrt((9x2-1)/x)
- sqrt9x2-1/x
- sqrt9x^2-1/x
- sqrt((9*x^2-1) divide by x)
- sqrt((9*x^2-1)/x)dx
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Similar expressions
- sqrt((9*x^2+1)/x)
Integral of sqrt((9*x^2-1)/x) dx
The solution
You have entered
[src]
1 / | | __________ | / 2 | / 9*x - 1 | / -------- dx | \/ x | / 0
$$\int\limits_{0}^{1} \sqrt{\frac{9 x^{2} - 1}{x}}\, dx$$
Integral(sqrt((9*x^2 - 1)/x), (x, 0, 1))
The answer
[src]
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|_ /-1/2, 1/4 | \
I*Gamma(1/4)* | | | 9|
2 1 \ 5/4 | /
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2*Gamma(5/4)
$$\frac{i \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {9} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}$$
=
=
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|_ /-1/2, 1/4 | \
I*Gamma(1/4)* | | | 9|
2 1 \ 5/4 | /
---------------------------------
2*Gamma(5/4)
$$\frac{i \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {9} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}$$
i*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 9)/(2*gamma(5/4))
Use the examples entering the upper and lower limits of integration.