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How to use it?
- Integral of d{x}:
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Integral of sin(5x)
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Integral of (x^3+1)^1/2
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Integral of x/(16x^4+1)
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Integral of t+1
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Identical expressions
- one /sqrt(one +x^ six)
- 1 divide by square root of (1 plus x to the power of 6)
- one divide by square root of (one plus x to the power of six)
- 1/√(1+x^6)
- 1/sqrt(1+x6)
- 1/sqrt1+x6
- 1/sqrt(1+x⁶)
- 1/sqrt1+x^6
- 1 divide by sqrt(1+x^6)
- 1/sqrt(1+x^6)dx
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Similar expressions
- 1/sqrt(1-x^6)
Integral of 1/sqrt(1+x^6) dx
The solution
You have entered
[src]
1 / | | 1 | ----------- dx | ________ | / 6 | \/ 1 + x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{x^{6} + 1}}\, dx$$
Integral(1/(sqrt(1 + x^6)), (x, 0, 1))
The answer (Indefinite)
[src]
_ / |_ /1/6, 1/2 | 6 pi*I\ | x*Gamma(1/6)* | | | x *e | | 1 2 1 \ 7/6 | / | ----------- dx = C + --------------------------------------- | ________ 6*Gamma(7/6) | / 6 | \/ 1 + x | /
$$\int \frac{1}{\sqrt{x^{6} + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6} \end{matrix}\middle| {x^{6} e^{i \pi}} \right)}}{6 \Gamma\left(\frac{7}{6}\right)}$$
The graph
The answer
[src]
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|_ /1/6, 1/2 | \
Gamma(1/6)* | | | -1|
2 1 \ 7/6 | /
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6*Gamma(7/6)
$$\frac{\Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6} \end{matrix}\middle| {-1} \right)}}{6 \Gamma\left(\frac{7}{6}\right)}$$
=
=
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|_ /1/6, 1/2 | \
Gamma(1/6)* | | | -1|
2 1 \ 7/6 | /
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6*Gamma(7/6)
$$\frac{\Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6} \end{matrix}\middle| {-1} \right)}}{6 \Gamma\left(\frac{7}{6}\right)}$$
gamma(1/6)*hyper((1/6, 1/2), (7/6,), -1)/(6*gamma(7/6))
Use the examples entering the upper and lower limits of integration.