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How to use it?
- Integral of d{x}:
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Integral of e^(3*x)
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Integral of x*exp(x)
- Integral of sin(ln(x))/x
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Integral of e^(x*(-2))
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Identical expressions
- cosx/x^(three / two)
- co sinus of e of x divide by x to the power of (3 divide by 2)
- co sinus of e of x divide by x to the power of (three divide by two)
- cosx/x(3/2)
- cosx/x3/2
- cosx/x^3/2
- cosx divide by x^(3 divide by 2)
- cosx/x^(3/2)dx
Integral of cosx/x^(3/2) dx
The solution
You have entered
[src]
oo / | | cos(x) | ------ dx | 3/2 | x | / 2
$$\int\limits_{2}^{\infty} \frac{\cos{\left(x \right)}}{x^{\frac{3}{2}}}\, dx$$
Integral(cos(x)/x^(3/2), (x, 2, oo))
The answer (Indefinite)
[src]
/ / | | | cos(x) | cos(x) | ------ dx = C + | ------ dx | 3/2 | 3/2 | x | x | | / /
$$\int \frac{\cos{\left(x \right)}}{x^{\frac{3}{2}}}\, dx = C + \int \frac{\cos{\left(x \right)}}{x^{\frac{3}{2}}}\, dx$$
The answer
[src]
/ / ____ / 2 \ \ \
| |2*\/ pi *S|------| + cos(2)|*Gamma(1/4)|
| | | ____| | |
___ ____ |Gamma(-1/4) \ \\/ pi / / |
\/ 2 *\/ pi *|----------- + ----------------------------------------|
| Gamma(3/4) ____ |
\ \/ pi *Gamma(5/4) /
---------------------------------------------------------------------
4
$$\frac{\sqrt{2} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{4}\right)}{\Gamma\left(\frac{3}{4}\right)} + \frac{\left(\cos{\left(2 \right)} + 2 \sqrt{\pi} S\left(\frac{2}{\sqrt{\pi}}\right)\right) \Gamma\left(\frac{1}{4}\right)}{\sqrt{\pi} \Gamma\left(\frac{5}{4}\right)}\right)}{4}$$
=
=
/ / ____ / 2 \ \ \
| |2*\/ pi *S|------| + cos(2)|*Gamma(1/4)|
| | | ____| | |
___ ____ |Gamma(-1/4) \ \\/ pi / / |
\/ 2 *\/ pi *|----------- + ----------------------------------------|
| Gamma(3/4) ____ |
\ \/ pi *Gamma(5/4) /
---------------------------------------------------------------------
4
$$\frac{\sqrt{2} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{4}\right)}{\Gamma\left(\frac{3}{4}\right)} + \frac{\left(\cos{\left(2 \right)} + 2 \sqrt{\pi} S\left(\frac{2}{\sqrt{\pi}}\right)\right) \Gamma\left(\frac{1}{4}\right)}{\sqrt{\pi} \Gamma\left(\frac{5}{4}\right)}\right)}{4}$$
sqrt(2)*sqrt(pi)*(gamma(-1/4)/gamma(3/4) + (2*sqrt(pi)*fresnels(2/sqrt(pi)) + cos(2))*gamma(1/4)/(sqrt(pi)*gamma(5/4)))/4
Use the examples entering the upper and lower limits of integration.