Mister Exam
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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 1/(e^(2*x))
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Integral of 1/(1+x^(1/2))
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Integral of (xe^x)dx
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Integral of x*dx
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Identical expressions
- sqrt((x- one)/(4sqrt(x)))
- square root of ((x minus 1) divide by (4 square root of (x)))
- square root of ((x minus one) divide by (4 square root of (x)))
- √((x-1)/(4√(x)))
- sqrtx-1/4sqrtx
- sqrt((x-1) divide by (4sqrt(x)))
- sqrt((x-1)/(4sqrt(x)))dx
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Similar expressions
- sqrt((x+1)/(4sqrt(x)))
- 1/sqrtx-1/4sqrtx^3
Integral of sqrt((x-1)/(4sqrt(x))) dx
The solution
You have entered
[src]
1 / | | _________ | / x - 1 | / ------- dx | / ___ | \/ 4*\/ x | / 0
$$\int\limits_{0}^{1} \sqrt{\frac{x - 1}{4 \sqrt{x}}}\, dx$$
Integral(sqrt((x - 1)/((4*sqrt(x)))), (x, 0, 1))
The answer (Indefinite)
[src]
/
|
| _______________
| / ___ 1
| / \/ x - ----- dx
/ | / ___
| | \/ \/ x
| _________ |
| / x - 1 /
| / ------- dx = C + --------------------------
| / ___ 2
| \/ 4*\/ x
|
/
$$\int \sqrt{\frac{x - 1}{4 \sqrt{x}}}\, dx = C + \frac{\int \sqrt{\sqrt{x} - \frac{1}{\sqrt{x}}}\, dx}{2}$$
The answer
[src]
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|_ /-1/2, 3/4 | \
I*Gamma(3/4)* | | | 1|
2 1 \ 7/4 | /
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2*Gamma(7/4)
$$\frac{i \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {1} \right)}}{2 \Gamma\left(\frac{7}{4}\right)}$$
=
=
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|_ /-1/2, 3/4 | \
I*Gamma(3/4)* | | | 1|
2 1 \ 7/4 | /
---------------------------------
2*Gamma(7/4)
$$\frac{i \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {1} \right)}}{2 \Gamma\left(\frac{7}{4}\right)}$$
i*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), 1)/(2*gamma(7/4))
Use the examples entering the upper and lower limits of integration.