Mister Exam

Integral of sqrt(3x+5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1               
  /               
 |                
 |    _________   
 |  \/ 3*x + 5  dx
 |                
/                 
0                 
$$\int\limits_{0}^{1} \sqrt{3 x + 5}\, dx$$
Integral(sqrt(3*x + 5), (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. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                   
 |                                 3/2
 |   _________          2*(3*x + 5)   
 | \/ 3*x + 5  dx = C + --------------
 |                            9       
/                                     
$$\int \sqrt{3 x + 5}\, dx = C + \frac{2 \left(3 x + 5\right)^{\frac{3}{2}}}{9}$$
The graph
The answer [src]
       ___        ___
  10*\/ 5    32*\/ 2 
- -------- + --------
     9          9    
$$- \frac{10 \sqrt{5}}{9} + \frac{32 \sqrt{2}}{9}$$
=
=
       ___        ___
  10*\/ 5    32*\/ 2 
- -------- + --------
     9          9    
$$- \frac{10 \sqrt{5}}{9} + \frac{32 \sqrt{2}}{9}$$
-10*sqrt(5)/9 + 32*sqrt(2)/9
Numerical answer [src]
2.5437949134379
2.5437949134379
The graph
Integral of sqrt(3x+5) dx

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