Mister Exam

Other calculators

Solving integrals/ x^2+3x+5

Integral of x^2+3x+5 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3                  
  /                  
 |                   
 |  / 2          \   
 |  \x  + 3*x + 5/ dx
 |                   
/                    
2
$$\int\limits_{2}^{3} \left(\left(x^{2} + 3 x\right) + 5\right)\, dx$$ 
Integral(x^2 + 3*x + 5, (x, 2, 3))
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    3*x 
 | \x  + 3*x + 5/ dx = C + 5*x + -- + ----
 |                               3     2  
/
$$\int \left(\left(x^{2} + 3 x\right) + 5\right)\, dx = C + \frac{x^{3}}{3} + \frac{3 x^{2}}{2} + 5 x$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
113/6
$$\frac{113}{6}$$ 
=
= 
113/6
$$\frac{113}{6}$$ 
113/6
Numerical answer [src] 
18.8333333333333
18.8333333333333

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

    © Mister Exam – Calculator