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Integral of 1/(1+(x+1)^(1/3))
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Identical expressions
one /(one +(x+ one)^(one / three))
1 divide by (1 plus (x plus 1) to the power of (1 divide by 3))
one divide by (one plus (x plus one) to the power of (one divide by three))
1/(1+(x+1)(1/3))
1/1+x+11/3
1/1+x+1^1/3
1 divide by (1+(x+1)^(1 divide by 3))
1/(1+(x+1)^(1/3))dx
Similar expressions
1/(1-(x+1)^(1/3))
1/(1+(x-1)^(1/3))

Solving integrals/ 1/(1+(x+1)^(1/3))

Integral of 1/(1+(x+1)^(1/3)) dx

The solution

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  1                   
  /                   
 |                    
 |          1         
 |  1*------------- dx
 |        3 _______   
 |    1 + \/ x + 1    
 |                    
/                     
0

\int\limits_{0}^{1} 1 \cdot \frac{1}{\sqrt[3]{x + 1} + 1}\, dx

Integral(1/(1 + (x + 1)^(1/3)), (x, 0, 1))

The answer (Indefinite) [src]

  /                                                                          
 |                                                                        2/3
 |         1                  3 _______        /    3 _______\   3*(1 + x)   
 | 1*------------- dx = C - 3*\/ 1 + x  + 3*log\1 + \/ 1 + x / + ------------
 |       3 _______                                                    2      
 |   1 + \/ x + 1                                                            
 |                                                                           
/

3\,\left(\log \left(\left(x+1\right)^{{{1}\over{3}}}+1\right)+{{ \left(x+1\right)^{{{2}\over{3}}}-2\,\left(x+1\right)^{{{1}\over{3}}} }\over{2}}\right)

Simplify

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The answer [src]

                                               2/3
3     3 ___                   /    3 ___\   3*2   
- - 3*\/ 2  - 3*log(2) + 3*log\1 + \/ 2 / + ------
2                                             2

3\,\log \left(2^{{{1}\over{3}}}+1\right)-3\,\log 2-3\,2^{{{1}\over{ 3}}}+{{3}\over{2^{{{1}\over{3}}}}}+{{3}\over{2}}

                                               2/3
3     3 ___                   /    3 ___\   3*2   
- - 3*\/ 2  - 3*log(2) + 3*log\1 + \/ 2 / + ------
2                                             2

- 3 \cdot \sqrt[3]{2} - 3 \log{\left(2 \right)} + \frac{3}{2} + \frac{3 \cdot 2^{\frac{2}{3}}}{2} + 3 \log{\left(1 + \sqrt[3]{2} \right)}

Упростить

Numerical answer [src]

0.467886523585338

0.467886523585338

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

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Identical expressions

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Integral of 1/(1+(x+1)^(1/3)) dx

Limits of integration:

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Piecewise:

The solution