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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(1+4x^2)
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Integral of (sec(x))^3
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Integral of x^2*e^(x^3)
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Integral of e^x²
- Limit of the function:
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sqrt(x)*sin(x^2)
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Identical expressions
- sqrt(x)*sin(x^ two)
- square root of (x) multiply by sinus of (x squared )
- square root of (x) multiply by sinus of (x to the power of two)
- √(x)*sin(x^2)
- sqrt(x)*sin(x2)
- sqrtx*sinx2
- sqrt(x)*sin(x²)
- sqrt(x)*sin(x to the power of 2)
- sqrt(x)sin(x^2)
- sqrt(x)sin(x2)
- sqrtxsinx2
- sqrtxsinx^2
- sqrt(x)*sin(x^2)dx
Integral of sqrt(x)*sin(x^2) dx
The solution
You have entered
[src]
oo / | | ___ / 2\ | \/ x *sin\x / dx | / 1
$$\int\limits_{1}^{\infty} \sqrt{x} \sin{\left(x^{2} \right)}\, dx$$
Integral(sqrt(x)*sin(x^2), (x, 1, oo))
The answer (Indefinite)
[src]
_ / | 4 \
/ 7/2 |_ | 7/8 | -x |
| x *Gamma(7/8)* | | | ----|
| ___ / 2\ 1 2 \3/2, 15/8 | 4 /
| \/ x *sin\x / dx = C + ---------------------------------------
| 4*Gamma(15/8)
/
$$\int \sqrt{x} \sin{\left(x^{2} \right)}\, dx = C + \frac{x^{\frac{7}{2}} \Gamma\left(\frac{7}{8}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{7}{8} \\ \frac{3}{2}, \frac{15}{8} \end{matrix}\middle| {- \frac{x^{4}}{4}} \right)}}{4 \Gamma\left(\frac{15}{8}\right)}$$
The answer
[src]
/ _ \
| |_ / 7/8 | \|
| 3/4 Gamma(-7/8)* | | | -1/4||
____ |2 *Gamma(7/8) 1 2 \3/2, 15/8 | /|
\/ pi *|--------------- + -----------------------------------|
| Gamma(5/8) ____ |
\ \/ pi *Gamma(1/8) /
--------------------------------------------------------------
4
$$\frac{\sqrt{\pi} \left(\frac{\Gamma\left(- \frac{7}{8}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{7}{8} \\ \frac{3}{2}, \frac{15}{8} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{1}{8}\right)} + \frac{2^{\frac{3}{4}} \Gamma\left(\frac{7}{8}\right)}{\Gamma\left(\frac{5}{8}\right)}\right)}{4}$$
=
=
/ _ \
| |_ / 7/8 | \|
| 3/4 Gamma(-7/8)* | | | -1/4||
____ |2 *Gamma(7/8) 1 2 \3/2, 15/8 | /|
\/ pi *|--------------- + -----------------------------------|
| Gamma(5/8) ____ |
\ \/ pi *Gamma(1/8) /
--------------------------------------------------------------
4
$$\frac{\sqrt{\pi} \left(\frac{\Gamma\left(- \frac{7}{8}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{7}{8} \\ \frac{3}{2}, \frac{15}{8} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{1}{8}\right)} + \frac{2^{\frac{3}{4}} \Gamma\left(\frac{7}{8}\right)}{\Gamma\left(\frac{5}{8}\right)}\right)}{4}$$
sqrt(pi)*(2^(3/4)*gamma(7/8)/gamma(5/8) + gamma(-7/8)*hyper((7/8,), (3/2, 15/8), -1/4)/(sqrt(pi)*gamma(1/8)))/4
Use the examples entering the upper and lower limits of integration.