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x^(-3/2)
Solving integrals/ x^(-3/2)

Integral of x^(-3/2) dx

Limits of integration:

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v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |   1     
 |  ---- dx
 |   3/2   
 |  x      
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/          
0
∫011x32 dx\int\limits_{0}^{1} \frac{1}{x^{\frac{3}{2}}}\, dx 
Integral(x^(-3/2), (x, 0, 1))
Detail solution

  1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

    ∫1x32 dx=−2x\int \frac{1}{x^{\frac{3}{2}}}\, dx = - \frac{2}{\sqrt{x}}

  2. Add the constant of integration:

    −2x+constant- \frac{2}{\sqrt{x}}+ \mathrm{constant}

The answer is:

−2x+constant- \frac{2}{\sqrt{x}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                   
 |                    
 |  1              2  
 | ---- dx = C - -----
 |  3/2            ___
 | x             \/ x 
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/
∫1x32 dx=C−2x\int \frac{1}{x^{\frac{3}{2}}}\, dx = C - \frac{2}{\sqrt{x}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-500000500000
Plot the graph f(x)
The answer [src] 
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∞\infty 
=
= 
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∞\infty 
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Numerical answer [src] 
7464448597.65649
7464448597.65649
The graph
Integral of x^(-3/2) dx

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

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