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How to use it?
- Integral of d{x}:
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Integral of 1/sqrt(1+x^4)
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Integral of x×arcsin(2x)
- Integral of ln(2cos(x))
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Integral of 5x^2dx
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Identical expressions
- one /sqrt(one +x^ four)
- 1 divide by square root of (1 plus x to the power of 4)
- one divide by square root of (one plus x to the power of four)
- 1/√(1+x^4)
- 1/sqrt(1+x4)
- 1/sqrt1+x4
- 1/sqrt(1+x⁴)
- 1/sqrt1+x^4
- 1 divide by sqrt(1+x^4)
- 1/sqrt(1+x^4)dx
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Similar expressions
- 1/sqrt(1-x^4)
Integral of 1/sqrt(1+x^4) dx
The solution
You have entered
[src]
10 / | | 1 | 1*----------- dx | ________ | / 4 | \/ 1 + x | / 2
$$\int\limits_{2}^{10} 1 \cdot \frac{1}{\sqrt{x^{4} + 1}}\, dx$$
Integral(1/sqrt(1 + x^4), (x, 2, 10))
The answer (Indefinite)
[src]
_ / |_ /1/4, 1/2 | 4 pi*I\ | x*Gamma(1/4)* | | | x *e | | 1 2 1 \ 5/4 | / | 1*----------- dx = C + --------------------------------------- | ________ 4*Gamma(5/4) | / 4 | \/ 1 + x | /
$$\int {{{1}\over{\sqrt{x^4+1}}}}{\;dx}$$
The graph
The answer
[src]
_ _
|_ /1/4, 1/2 | pi*I\ |_ /1/4, 1/2 | pi*I\
Gamma(1/4)* | | | 16*e | 5*Gamma(1/4)* | | | 10000*e |
2 1 \ 5/4 | / 2 1 \ 5/4 | /
- ------------------------------------- + ------------------------------------------
2*Gamma(5/4) 2*Gamma(5/4)
$$\int_{2}^{10}{{{1}\over{\sqrt{x^4+1}}}\;dx}$$
=
=
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|_ /1/4, 1/2 | pi*I\ |_ /1/4, 1/2 | pi*I\
Gamma(1/4)* | | | 16*e | 5*Gamma(1/4)* | | | 10000*e |
2 1 \ 5/4 | / 2 1 \ 5/4 | /
- ------------------------------------- + ------------------------------------------
2*Gamma(5/4) 2*Gamma(5/4)
$$- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {16 e^{i \pi}} \right)}}{2 \Gamma\left(\frac{5}{4}\right)} + \frac{5 \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {10000 e^{i \pi}} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}$$
The graph
Use the examples entering the upper and lower limits of integration.