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Solving integrals/ sqrt(x)*sin(x^2)

Integral of sqrt(x)*sin(x^2) dx

Limits of integration:

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The solution

You have entered [src] 
 oo                 
  /                 
 |                  
 |    ___    / 2\   
 |  \/ x *sin\x / dx
 |                  
/                   
1
∫1∞xsin⁡(x2) dx\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)             
/
∫xsin⁡(x2) dx=C+x72Γ(78)1F2(7832,158|−x44)4Γ(158)\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)}
Simplify
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
π(Γ(−78)1F2(7832,158|−14)πΓ(18)+234Γ(78)Γ(58))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
π(Γ(−78)1F2(7832,158|−14)πΓ(18)+234Γ(78)Γ(58))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.

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