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sqrt(x+1)
Solving integrals/ sqrt(x+1)

Integral of sqrt(x+1) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1             
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 |  \/ x + 1  dx
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0
∫01x+1 dx\int\limits_{0}^{1} \sqrt{x + 1}\, dx 
Integral(sqrt(x + 1), (x, 0, 1))
Detail solution

  1. Let u=x+1u = x + 1.

    Then let du=dxdu = dx and substitute dudu:

    ∫u du\int \sqrt{u}\, du

    1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫u du=2u323\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}

    Now substitute uu back in:

    2(x+1)323\frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3}

  2. Now simplify:

    2(x+1)323\frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3}

  3. Add the constant of integration:

    2(x+1)323+constant\frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer is:

2(x+1)323+constant\frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                               
 |                             3/2
 |   _______          2*(x + 1)   
 | \/ x + 1  dx = C + ------------
 |                         3      
/
∫x+1 dx=C+2(x+1)323\int \sqrt{x + 1}\, dx = C + \frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
          ___
  2   4*\/ 2 
- - + -------
  3      3
−23+423- \frac{2}{3} + \frac{4 \sqrt{2}}{3} 
=
= 
          ___
  2   4*\/ 2 
- - + -------
  3      3
−23+423- \frac{2}{3} + \frac{4 \sqrt{2}}{3} 
-2/3 + 4*sqrt(2)/3
Numerical answer [src] 
1.21895141649746
1.21895141649746
The graph
Integral of sqrt(x+1) dx

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

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