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How to use it?
- Integral of d{x}:
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Integral of x*e^(x*(-2))
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Integral of e^(x*(-3))*dx
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Integral of (x+3)/(x^2-5x+6)
- Integral of (sin(2x)+cos(2x))/(1+tg(x))
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Identical expressions
- one /sqrt(one +x^ three)
- 1 divide by square root of (1 plus x cubed )
- one divide by square root of (one plus x to the power of three)
- 1/√(1+x^3)
- 1/sqrt(1+x3)
- 1/sqrt1+x3
- 1/sqrt(1+x³)
- 1/sqrt(1+x to the power of 3)
- 1/sqrt1+x^3
- 1 divide by sqrt(1+x^3)
- 1/sqrt(1+x^3)dx
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Similar expressions
- 1/sqrt(1-x^3)
Integral of 1/sqrt(1+x^3) dx
The solution
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[src]
1 / | | 1 | ----------- dx | ________ | / 3 | \/ 1 + x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{x^{3} + 1}}\, dx$$
Integral(1/(sqrt(1 + x^3)), (x, 0, 1))
The answer (Indefinite)
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_ / |_ /1/3, 1/2 | 3 pi*I\ | x*Gamma(1/3)* | | | x *e | | 1 2 1 \ 4/3 | / | ----------- dx = C + --------------------------------------- | ________ 3*Gamma(4/3) | / 3 | \/ 1 + x | /
$$\int \frac{1}{\sqrt{x^{3} + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
The graph
The answer
[src]
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|_ /1/3, 1/2 | \
Gamma(1/3)* | | | -1|
2 1 \ 4/3 | /
-------------------------------
3*Gamma(4/3)
$$\frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {-1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
=
=
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|_ /1/3, 1/2 | \
Gamma(1/3)* | | | -1|
2 1 \ 4/3 | /
-------------------------------
3*Gamma(4/3)
$$\frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {-1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
gamma(1/3)*hyper((1/3, 1/2), (4/3,), -1)/(3*gamma(4/3))
The graph
Use the examples entering the upper and lower limits of integration.