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  • Identical expressions

  • ((sinx)^ three *sqrt(one +(sinx)^ two))/sqrt(one +(sinx)^ two)
  • (( sinus of x) cubed multiply by square root of (1 plus ( sinus of x) squared )) divide by square root of (1 plus ( sinus of x) squared )
  • (( sinus of x) to the power of three multiply by square root of (one plus ( sinus of x) to the power of two)) divide by square root of (one plus ( sinus of x) to the power of two)
  • ((sinx)^3*√(1+(sinx)^2))/√(1+(sinx)^2)
  • ((sinx)3*sqrt(1+(sinx)2))/sqrt(1+(sinx)2)
  • sinx3*sqrt1+sinx2/sqrt1+sinx2
  • ((sinx)³*sqrt(1+(sinx)²))/sqrt(1+(sinx)²)
  • ((sinx) to the power of 3*sqrt(1+(sinx) to the power of 2))/sqrt(1+(sinx) to the power of 2)
  • ((sinx)^3sqrt(1+(sinx)^2))/sqrt(1+(sinx)^2)
  • ((sinx)3sqrt(1+(sinx)2))/sqrt(1+(sinx)2)
  • sinx3sqrt1+sinx2/sqrt1+sinx2
  • sinx^3sqrt1+sinx^2/sqrt1+sinx^2
  • ((sinx)^3*sqrt(1+(sinx)^2)) divide by sqrt(1+(sinx)^2)
  • ((sinx)^3*sqrt(1+(sinx)^2))/sqrt(1+(sinx)^2)dx

  • Similar expressions

  • ((sinx)^3*sqrt(1-(sinx)^2))/sqrt(1+(sinx)^2)
  • ((sinx)^3*sqrt(1+(sinx)^2))/sqrt(1-(sinx)^2)
Solving integrals/ ((sinx)^3*sqrt(1+(sinx)^2))/sqrt(1+(sinx)^2)

Integral of ((sinx)^3*sqrt(1+(sinx)^2))/sqrt(1+(sinx)^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                            
  /                            
 |                             
 |             _____________   
 |     3      /        2       
 |  sin (x)*\/  1 + sin (x)    
 |  ------------------------ dx
 |         _____________       
 |        /        2           
 |      \/  1 + sin (x)        
 |                             
/                              
0
$$\int\limits_{0}^{1} \frac{\sqrt{\sin^{2}{\left(x \right)} + 1} \sin^{3}{\left(x \right)}}{\sqrt{\sin^{2}{\left(x \right)} + 1}}\, dx$$ 
Integral((sin(x)^3*sqrt(1 + sin(x)^2))/sqrt(1 + sin(x)^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                  
 |                                                   
 |            _____________                          
 |    3      /        2                          3   
 | sin (x)*\/  1 + sin (x)                    cos (x)
 | ------------------------ dx = C - cos(x) + -------
 |        _____________                          3   
 |       /        2                                  
 |     \/  1 + sin (x)                               
 |                                                   
/
$$\int \frac{\sqrt{\sin^{2}{\left(x \right)} + 1} \sin^{3}{\left(x \right)}}{\sqrt{\sin^{2}{\left(x \right)} + 1}}\, dx = C + \frac{\cos^{3}{\left(x \right)}}{3} - \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                3   
2            cos (1)
- - cos(1) + -------
3               3
$$- \cos{\left(1 \right)} + \frac{\cos^{3}{\left(1 \right)}}{3} + \frac{2}{3}$$ 
=
= 
                3   
2            cos (1)
- - cos(1) + -------
3               3
$$- \cos{\left(1 \right)} + \frac{\cos^{3}{\left(1 \right)}}{3} + \frac{2}{3}$$ 
2/3 - cos(1) + cos(1)^3/3
Numerical answer [src] 
0.178940562548858
0.178940562548858

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

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