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Derivative of:
(x+1)^(1/2)
Graphing y =:
(x+1)^(1/2)
Identical expressions
(x+ one)^(one / two)
(x plus 1) to the power of (1 divide by 2)
(x plus one) to the power of (one divide by two)
(x+1)(1/2)
x+11/2
x+1^1/2
(x+1)^(1 divide by 2)
(x+1)^(1/2)dx
Similar expressions
(x-1)^(1/2)
(x^1/2-1)(x+1)^1/2
4/((3x+1)^1/2)-3/(2x-5)
1/(2x+(3x+1)^1/2)

Solving integrals/ (x+1)^(1/2)

Integral of (x+1)^(1/2) dx

The solution

You have entered [src]

  1             
  /             
 |              
 |    _______   
 |  \/ x + 1  dx
 |              
/               
0

$$\int\limits_{0}^{1} \sqrt{x + 1}\, dx$$

Integral(sqrt(x + 1), (x, 0, 1))

Detail solution

Let $u = x + 1$ .

Then let $du = dx$ and substitute $du$ :

$\int \sqrt{u}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
Now substitute $u$ back in:

$\frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3}$
Now simplify:

$\frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \sqrt{x + 1}\, dx = C + \frac{2 \left(x + 1\right)^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

          ___
  2   4*\/ 2 
- - + -------
  3      3

$$- \frac{2}{3} + \frac{4 \sqrt{2}}{3}$$

          ___
  2   4*\/ 2 
- - + -------
  3      3

$$- \frac{2}{3} + \frac{4 \sqrt{2}}{3}$$

-2/3 + 4*sqrt(2)/3

Numerical answer [src]

1.21895141649746

1.21895141649746

The graph

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

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Identical expressions

Similar expressions

Integral of (x+1)^(1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution