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Solving integrals/ |sinx|/x^p

Integral of |sinx|/x^p dx

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The solution

You have entered [src] 
  1            
  /            
 |             
 |  |sin(x)|   
 |  -------- dx
 |      p      
 |     x       
 |             
/              
0
∫01∣sin⁡(x)∣xp dx\int\limits_{0}^{1} \frac{\left|{\sin{\left(x \right)}}\right|}{x^{p}}\, dx 
Integral(Abs(sin(x))/x^p, (x, 0, 1))
The answer (Indefinite) [src] 
  /                    /               
 |                    |                
 | |sin(x)|           |  -p            
 | -------- dx = C +  | x  *|sin(x)| dx
 |     p              |                
 |    x              /                 
 |                                     
/
∫∣sin⁡(x)∣xp dx=C+∫x−p∣sin⁡(x)∣ dx\int \frac{\left|{\sin{\left(x \right)}}\right|}{x^{p}}\, dx = C + \int x^{- p} \left|{\sin{\left(x \right)}}\right|\, dx
Simplify
The answer [src] 
                                     
                  /      p    |     \
               _  |  1 - -    |     |
     /    p\  |_  |      2    |     |
Gamma|1 - -|* |   |           | -1/4|
     \    2/ 1  2 |         p |     |
                  |3/2, 2 - - |     |
                  \         2 |     /
-------------------------------------
                   /    p\           
            2*Gamma|2 - -|           
                   \    2/
Γ(1−p2)1F2(1−p232,2−p2|−14)2Γ(2−p2)\frac{\Gamma\left(1 - \frac{p}{2}\right) {{}_{1}F_{2}\left(\begin{matrix} 1 - \frac{p}{2} \\ \frac{3}{2}, 2 - \frac{p}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{2 \Gamma\left(2 - \frac{p}{2}\right)} 
=
= 
                                     
                  /      p    |     \
               _  |  1 - -    |     |
     /    p\  |_  |      2    |     |
Gamma|1 - -|* |   |           | -1/4|
     \    2/ 1  2 |         p |     |
                  |3/2, 2 - - |     |
                  \         2 |     /
-------------------------------------
                   /    p\           
            2*Gamma|2 - -|           
                   \    2/
Γ(1−p2)1F2(1−p232,2−p2|−14)2Γ(2−p2)\frac{\Gamma\left(1 - \frac{p}{2}\right) {{}_{1}F_{2}\left(\begin{matrix} 1 - \frac{p}{2} \\ \frac{3}{2}, 2 - \frac{p}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{2 \Gamma\left(2 - \frac{p}{2}\right)} 
gamma(1 - p/2)*hyper((1 - p/2,), (3/2, 2 - p/2), -1/4)/(2*gamma(2 - p/2))

    Use the examples entering the upper and lower limits of integration.

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