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1/√(x+1)
Solving integrals/ 1/√(x+1)

Integral of 1/√(x+1) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

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

  1. Let u=x+1u = \sqrt{x + 1}.

    Then let du=dx2x+1du = \frac{dx}{2 \sqrt{x + 1}} and substitute 2du2 du:

    ∫2 du\int 2\, du

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

      False\text{False}

      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:

    2x+12 \sqrt{x + 1}

  2. Now simplify:

    2x+12 \sqrt{x + 1}

  3. Add the constant of integration:

    2x+1+constant2 \sqrt{x + 1}+ \mathrm{constant}

The answer is:

2x+1+constant2 \sqrt{x + 1}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                              
 |                               
 |     1                  _______
 | --------- dx = C + 2*\/ x + 1 
 |   _______                     
 | \/ x + 1                      
 |                               
/
∫1x+1 dx=C+2x+1\int \frac{1}{\sqrt{x + 1}}\, dx = C + 2 \sqrt{x + 1}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.05.0
Plot the graph f(x)
The answer [src] 
         ___
-2 + 2*\/ 2
−2+22-2 + 2 \sqrt{2} 
=
= 
         ___
-2 + 2*\/ 2
−2+22-2 + 2 \sqrt{2} 
-2 + 2*sqrt(2)
Numerical answer [src] 
0.82842712474619
0.82842712474619
The graph
Integral of 1/√(x+1) dx

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

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