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x√x^2+1
Solving integrals/ x√x^2+1

Integral of x√x^2+1 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Integrate term-by-term:

    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:

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

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                              
 |                               
 | /       2    \               3
 | |    ___     |              x 
 | \x*\/ x   + 1/ dx = C + x + --
 |                             3 
/
$$\int \left(x \left(\sqrt{x}\right)^{2} + 1\right)\, dx = C + \frac{x^{3}}{3} + x$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
4/3
$$\frac{4}{3}$$ 
=
= 
4/3
$$\frac{4}{3}$$ 
4/3
Numerical answer [src] 
1.33333333333333
1.33333333333333
The graph
Integral of x√x^2+1 dx

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

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