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Solving integrals/ x^2+4*x+5

Integral of x^2+4*x+5 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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 |  / 2          \   
 |  \x  + 4*x + 5/ dx
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0
$$\int\limits_{0}^{1} \left(\left(x^{2} + 4 x\right) + 5\right)\, dx$$ 
Integral(x^2 + 4*x + 5, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

      1. The integral of is when :

      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:

      The result is:

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

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                       
 |                                       3
 | / 2          \             2         x 
 | \x  + 4*x + 5/ dx = C + 2*x  + 5*x + --
 |                                      3 
/
$$\int \left(\left(x^{2} + 4 x\right) + 5\right)\, dx = C + \frac{x^{3}}{3} + 2 x^{2} + 5 x$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
22/3
$$\frac{22}{3}$$ 
=
= 
22/3
$$\frac{22}{3}$$ 
22/3
Numerical answer [src] 
7.33333333333333
7.33333333333333

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

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