Mister Exam

Other calculators

Solving integrals/ 3*dx/sqrt(2*x+1)

Integral of 3*dx/sqrt(2*x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  4               
  /               
 |                
 |       3        
 |  ----------- dx
 |    _________   
 |  \/ 2*x + 1    
 |                
/                 
0
∫0432x+1 dx\int\limits_{0}^{4} \frac{3}{\sqrt{2 x + 1}}\, dx 
Integral(3/sqrt(2*x + 1), (x, 0, 4))
Detail solution

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

    ∫32x+1 dx=3∫12x+1 dx\int \frac{3}{\sqrt{2 x + 1}}\, dx = 3 \int \frac{1}{\sqrt{2 x + 1}}\, dx

    1. Let u=2x+1u = \sqrt{2 x + 1}.

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

      ∫1 du\int 1\, du

      1. The integral of a constant is the constant times the variable of integration:

        ∫1 du=u\int 1\, du = u

      Now substitute uu back in:

      2x+1\sqrt{2 x + 1}

    So, the result is: 32x+13 \sqrt{2 x + 1}

  2. Now simplify:

    32x+13 \sqrt{2 x + 1}

  3. Add the constant of integration:

    32x+1+constant3 \sqrt{2 x + 1}+ \mathrm{constant}

The answer is:

32x+1+constant3 \sqrt{2 x + 1}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                                   
 |      3                   _________
 | ----------- dx = C + 3*\/ 2*x + 1 
 |   _________                       
 | \/ 2*x + 1                        
 |                                   
/
∫32x+1 dx=C+32x+1\int \frac{3}{\sqrt{2 x + 1}}\, dx = C + 3 \sqrt{2 x + 1}
Simplify
The graph
0.04.00.51.01.52.02.53.03.5010
Plot the graph f(x)
The answer [src] 
6
66 
=
= 
6
66 
6
Numerical answer [src] 
6.0
6.0

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

    © Mister Exam – Calculator