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cosx/sqrt(sinx)
Solving integrals/ cosx/sqrt(sinx)

Integral of cosx/sqrt(sinx) dx

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The solution

You have entered [src] 
  1              
  /              
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 |    cos(x)     
 |  ---------- dx
 |    ________   
 |  \/ sin(x)    
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0
∫01cos⁡(x)sin⁡(x) dx\int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}\, dx 
Integral(cos(x)/(sqrt(sin(x))), (x, 0, 1))
Detail solution

  1. Let u=sin⁡(x)u = \sqrt{\sin{\left(x \right)}}.

    Then let du=cos⁡(x)dx2sin⁡(x)du = \frac{\cos{\left(x \right)} dx}{2 \sqrt{\sin{\left(x \right)}}} and substitute 2du2 du:

    ∫4 du\int 4\, du

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫2 du=2∫1 du\int 2\, du = 2 \int 1\, du

      1. The integral of a constant is the constant times the variable of integration:

        ∫1 du=u\int 1\, du = u

      So, the result is: 2u2 u

    Now substitute uu back in:

    2sin⁡(x)2 \sqrt{\sin{\left(x \right)}}

  2. Add the constant of integration:

    2sin⁡(x)+constant2 \sqrt{\sin{\left(x \right)}}+ \mathrm{constant}

The answer is:

2sin⁡(x)+constant2 \sqrt{\sin{\left(x \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                
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 |   cos(x)                ________
 | ---------- dx = C + 2*\/ sin(x) 
 |   ________                      
 | \/ sin(x)                       
 |                                 
/
2 sin⁡x2\,\sqrt{\sin x}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900100
Plot the graph f(x)
The answer [src] 
    ________
2*\/ sin(1)
2 sin⁡12\,\sqrt{\sin 1} 
=
= 
    ________
2*\/ sin(1)
2sin⁡(1)2 \sqrt{\sin{\left(1 \right)}}
Simplify
Numerical answer [src] 
1.83463455128634
1.83463455128634
The graph
Integral of cosx/sqrt(sinx) dx

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

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