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How to use it?
- Integral of d{x}:
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Integral of cosx^2
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Integral of sinh(x)
- Integral of xcos(nx)
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Integral of arcsinx+arccosx
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Identical expressions
- e^(x^ four / four)
- e to the power of (x to the power of 4 divide by 4)
- e to the power of (x to the power of four divide by four)
- e(x4/4)
- ex4/4
- e^(x⁴/4)
- e^x^4/4
- e^(x^4 divide by 4)
- e^(x^4/4)dx
Integral of e^(x^4/4) dx
The solution
You have entered
[src]
1 / | | 4 | x | -- | 4 | E dx | / 0
$$\int\limits_{0}^{1} e^{\frac{x^{4}}{4}}\, dx$$
Integral(E^(x^4/4), (x, 0, 1))
The answer (Indefinite)
[src]
/ | -pi*I | 4 ------ / 4 pi*I\ | x ___ 4 | x *e | | -- \/ 2 *e *Gamma(1/4)*lowergamma|1/4, --------| | 4 \ 4 / | E dx = C + -------------------------------------------------- | 16*Gamma(5/4) /
$$\int e^{\frac{x^{4}}{4}}\, dx = C + \frac{\sqrt{2} e^{- \frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, \frac{x^{4} e^{i \pi}}{4}\right)}{16 \Gamma\left(\frac{5}{4}\right)}$$
The graph
The answer
[src]
-pi*I
------ / pi*I\
___ 4 | e |
\/ 2 *e *Gamma(1/4)*lowergamma|1/4, -----|
\ 4 /
-----------------------------------------------
16*Gamma(5/4)
$$\frac{\sqrt{2} e^{- \frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, \frac{e^{i \pi}}{4}\right)}{16 \Gamma\left(\frac{5}{4}\right)}$$
=
=
-pi*I
------ / pi*I\
___ 4 | e |
\/ 2 *e *Gamma(1/4)*lowergamma|1/4, -----|
\ 4 /
-----------------------------------------------
16*Gamma(5/4)
$$\frac{\sqrt{2} e^{- \frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, \frac{e^{i \pi}}{4}\right)}{16 \Gamma\left(\frac{5}{4}\right)}$$
sqrt(2)*exp(-pi*i/4)*gamma(1/4)*lowergamma(1/4, exp_polar(pi*i)/4)/(16*gamma(5/4))
Use the examples entering the upper and lower limits of integration.