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sinh^3x
Solving integrals/ sinh^3x

Integral of sinh^3x dx

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The solution

You have entered [src] 
  1            
  /            
 |             
 |      3      
 |  sinh (x) dx
 |             
/              
0
$$\int\limits_{0}^{1} \sinh^{3}{\left(x \right)}\, dx$$ 
Integral(sinh(x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                               
 |                         3                      
 |     3             2*cosh (x)       2           
 | sinh (x) dx = C - ---------- + sinh (x)*cosh(x)
 |                       3                        
/
$$\int \sinh^{3}{\left(x \right)}\, dx = C + \sinh^{2}{\left(x \right)} \cosh{\left(x \right)} - \frac{2 \cosh^{3}{\left(x \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
          3                      
2   2*cosh (1)       2           
- - ---------- + sinh (1)*cosh(1)
3       3
$$- \frac{2 \cosh^{3}{\left(1 \right)}}{3} + \frac{2}{3} + \sinh^{2}{\left(1 \right)} \cosh{\left(1 \right)}$$ 
=
= 
          3                      
2   2*cosh (1)       2           
- - ---------- + sinh (1)*cosh(1)
3       3
$$- \frac{2 \cosh^{3}{\left(1 \right)}}{3} + \frac{2}{3} + \sinh^{2}{\left(1 \right)} \cosh{\left(1 \right)}$$ 
2/3 - 2*cosh(1)^3/3 + sinh(1)^2*cosh(1)
Numerical answer [src] 
0.348328023536714
0.348328023536714
The graph
Integral of sinh^3x dx

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

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