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Identical expressions
x^ two +7x+ twelve
x squared plus 7x plus 12
x to the power of two plus 7x plus twelve
x2+7x+12
x²+7x+12
x to the power of 2+7x+12
x^2+7x+12dx
Similar expressions
x^2+7x-12
x^2-7x+12

Integral of x^2+7x+12 dx

The solution

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  1                   
  /                   
 |                    
 |  / 2           \   
 |  \x  + 7*x + 12/ dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(\left(x^{2} + 7 x\right) + 12\right)\, dx$$

Integral(x^2 + 7*x + 12, (x, 0, 1))

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:
    
    $\int 7 x\, dx = 7 \int x\, dx$
    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: $\frac{7 x^{2}}{2}$
  The result is: $\frac{x^{3}}{3} + \frac{7 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 12\, dx = 12 x$
The result is: $\frac{x^{3}}{3} + \frac{7 x^{2}}{2} + 12 x$
Now simplify:

$\frac{x \left(2 x^{2} + 21 x + 72\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} + 21 x + 72\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} + 21 x + 72\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                  3      2
 | / 2           \                 x    7*x 
 | \x  + 7*x + 12/ dx = C + 12*x + -- + ----
 |                                 3     2  
/

$$\int \left(\left(x^{2} + 7 x\right) + 12\right)\, dx = C + \frac{x^{3}}{3} + \frac{7 x^{2}}{2} + 12 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

95/6

$$\frac{95}{6}$$

95/6

$$\frac{95}{6}$$

95/6

Numerical answer [src]

15.8333333333333

15.8333333333333

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

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Integral of x^2+7x+12 dx

Limits of integration:

The graph:

Piecewise:

The solution