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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x/(1+x)
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Integral of x/e^x
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Integral of 6
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Integral of x^1
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Identical expressions
- cosh(two x^2)
- hyperbolic co sinus of e of ine of (2x squared )
- hyperbolic co sinus of e of ine of (two x squared )
- cosh(2x2)
- cosh2x2
- cosh(2x²)
- cosh(2x to the power of 2)
- cosh2x^2
- cosh(2x^2)dx
Integral of cosh(2x^2) dx
The solution
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[src]
1 / | | / 2\ | cosh\2*x / dx | / 0
$$\int\limits_{0}^{1} \cosh{\left(2 x^{2} \right)}\, dx$$
Integral(cosh(2*x^2), (x, 0, 1))
The answer (Indefinite)
[src]
/ pi*I\
-pi*I | ----|
------ | 4 |
____ 4 |2*x*e |
/ \/ pi *e *C|---------|*Gamma(1/4)
| | ____ |
| / 2\ \ \/ pi /
| cosh\2*x / dx = C + --------------------------------------
| 8*Gamma(5/4)
/
$$\int \cosh{\left(2 x^{2} \right)}\, dx = C + \frac{\sqrt{\pi} e^{- \frac{i \pi}{4}} C\left(\frac{2 x e^{\frac{i \pi}{4}}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)}$$
The graph
The answer
[src]
/ pi*I\
-pi*I | ----|
------ | 4 |
____ 4 |2*e |
\/ pi *e *C|-------|*Gamma(1/4)
| ____|
\ \/ pi /
------------------------------------
8*Gamma(5/4)
$$\frac{\sqrt{\pi} e^{- \frac{i \pi}{4}} C\left(\frac{2 e^{\frac{i \pi}{4}}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)}$$
=
=
/ pi*I\
-pi*I | ----|
------ | 4 |
____ 4 |2*e |
\/ pi *e *C|-------|*Gamma(1/4)
| ____|
\ \/ pi /
------------------------------------
8*Gamma(5/4)
$$\frac{\sqrt{\pi} e^{- \frac{i \pi}{4}} C\left(\frac{2 e^{\frac{i \pi}{4}}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)}$$
sqrt(pi)*exp(-pi*i/4)*fresnelc(2*exp(pi*i/4)/sqrt(pi))*gamma(1/4)/(8*gamma(5/4))
Use the examples entering the upper and lower limits of integration.