Mister Exam

Integral of sqrt(3+2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1               
  /               
 |                
 |    _________   
 |  \/ 3 + 2*x  dx
 |                
/                 
0                 
$$\int\limits_{0}^{1} \sqrt{2 x + 3}\, dx$$
Integral(sqrt(3 + 2*x), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

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

      1. The integral of is when :

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                 
 |                               3/2
 |   _________          (3 + 2*x)   
 | \/ 3 + 2*x  dx = C + ------------
 |                           3      
/                                   
$$\int \sqrt{2 x + 3}\, dx = C + \frac{\left(2 x + 3\right)^{\frac{3}{2}}}{3}$$
The graph
The answer [src]
              ___
    ___   5*\/ 5 
- \/ 3  + -------
             3   
$$- \sqrt{3} + \frac{5 \sqrt{5}}{3}$$
=
=
              ___
    ___   5*\/ 5 
- \/ 3  + -------
             3   
$$- \sqrt{3} + \frac{5 \sqrt{5}}{3}$$
-sqrt(3) + 5*sqrt(5)/3
Numerical answer [src]
1.99472915493077
1.99472915493077
The graph
Integral of sqrt(3+2x) dx

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