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Derivative of:
x^2+3x+5
Graphing y =:
x^2+3x+5
Identical expressions
x^ two +3x+ five
x squared plus 3x plus 5
x to the power of two plus 3x plus five
x2+3x+5
x²+3x+5
x to the power of 2+3x+5
x^2+3x+5dx
Similar expressions
x^2+3x-5
x^2-3x+5

Integral of x^2+3x+5 dx

The solution

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  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

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x\, dx = 3 \int x\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    So, the result is: $\frac{3 x^{2}}{2}$
  The result is: $\frac{x^{3}}{3} + \frac{3 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 5\, dx = 5 x$
The result is: $\frac{x^{3}}{3} + \frac{3 x^{2}}{2} + 5 x$
Now simplify:

$\frac{x \left(2 x^{2} + 9 x + 30\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} + 9 x + 30\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} + 9 x + 30\right)}{6}+ \mathrm{constant}$

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.

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Identical expressions

Similar expressions

Integral of x^2+3x+5 dx

Limits of integration:

The graph:

Piecewise:

The solution