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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of e^(x^2)
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Integral of e^(-x)
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Integral of sin(x)^3
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Integral of cos(x/2)
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Identical expressions
- e^(x^ two *x*dx)dx
- e to the power of (x squared multiply by x multiply by dx)dx
- e to the power of (x to the power of two multiply by x multiply by dx)dx
- e(x2*x*dx)dx
- ex2*x*dxdx
- e^(x²*x*dx)dx
- e to the power of (x to the power of 2*x*dx)dx
- e^(x^2xdx)dx
- e(x2xdx)dx
- ex2xdxdx
- e^x^2xdxdx
Integral of e^(x^2*x*dx)dx dx
The solution
You have entered
[src]
1 / | | 2 | x *x | E dx | / 0
$$\int\limits_{0}^{1} e^{x x^{2}}\, dx$$
Integral(E^(x^2*x), (x, 0, 1))
The answer (Indefinite)
[src]
/ -pi*I | ------ | 2 3 / 3 pi*I\ | x *x e *Gamma(1/3)*lowergamma\1/3, x *e / | E dx = C + -------------------------------------------- | 9*Gamma(4/3) /
$$\int e^{x x^{2}}\, dx = C + \frac{e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) \gamma\left(\frac{1}{3}, x^{3} e^{i \pi}\right)}{9 \Gamma\left(\frac{4}{3}\right)}$$
The graph
The answer
[src]
-pi*I
------
3 / pi*I\
e *Gamma(1/3)*lowergamma\1/3, e /
-----------------------------------------
9*Gamma(4/3)
$$\frac{e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) \gamma\left(\frac{1}{3}, e^{i \pi}\right)}{9 \Gamma\left(\frac{4}{3}\right)}$$
=
=
-pi*I
------
3 / pi*I\
e *Gamma(1/3)*lowergamma\1/3, e /
-----------------------------------------
9*Gamma(4/3)
$$\frac{e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) \gamma\left(\frac{1}{3}, e^{i \pi}\right)}{9 \Gamma\left(\frac{4}{3}\right)}$$
exp(-pi*i/3)*gamma(1/3)*lowergamma(1/3, exp_polar(pi*i))/(9*gamma(4/3))
Use the examples entering the upper and lower limits of integration.