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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of x^2*e^3x
- Integral of x*atan(x)/sqrt(1+x^3)
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Integral of x^2*e^(x/2)*dx
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Integral of x^2*(9-x^2)^(-1/2)
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Identical expressions
- sqrt(one + one /(x^ four))
- square root of (1 plus 1 divide by (x to the power of 4))
- square root of (one plus one divide by (x to the power of four))
- √(1+1/(x^4))
- sqrt(1+1/(x4))
- sqrt1+1/x4
- sqrt(1+1/(x⁴))
- sqrt1+1/x^4
- sqrt(1+1 divide by (x^4))
- sqrt(1+1/(x^4))dx
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Similar expressions
- sqrt(1-1/(x^4))
Integral of sqrt(1+1/(x^4)) dx
The solution
You have entered
[src]
1 / | | ________ | / 1 | / 1 + -- dx | / 4 | \/ x | / 0
$$\int\limits_{0}^{1} \sqrt{1 + \frac{1}{x^{4}}}\, dx$$
Integral(sqrt(1 + 1/(x^4)), (x, 0, 1))
The answer (Indefinite)
[src]
_ / | pi*I\
/ |_ |-1/2, -1/4 | e |
| x*Gamma(-1/4)* | | | -----|
| ________ 2 1 | 3/4 | 4 |
| / 1 \ | x /
| / 1 + -- dx = C - ---------------------------------------
| / 4 4*Gamma(3/4)
| \/ x
|
/
$$\int \sqrt{1 + \frac{1}{x^{4}}}\, dx = C - \frac{x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{e^{i \pi}}{x^{4}}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}$$
The graph
The answer
[src]
_
|_ /-1/2, -1/4 | \
-Gamma(-1/4)* | | | -1|
2 1 \ 3/4 | /
------------------------------------
4*Gamma(3/4)
$$- \frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {-1} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}$$
=
=
_
|_ /-1/2, -1/4 | \
-Gamma(-1/4)* | | | -1|
2 1 \ 3/4 | /
------------------------------------
4*Gamma(3/4)
$$- \frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {-1} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}$$
-gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), -1)/(4*gamma(3/4))
The graph
Use the examples entering the upper and lower limits of integration.