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Integral of d{x}:
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Integral of x^3*ln(x)
Integral of x(x^2+3)
Integral of x^2*lnx
Derivative of:
x^2-7x+6
Identical expressions
x^ two -7x+ six
x squared minus 7x plus 6
x to the power of two minus 7x plus six
x2-7x+6
x²-7x+6
x to the power of 2-7x+6
x^2-7x+6dx
Similar expressions
x^2-7x-6
x^2+7x+6

Solving integrals/ x^2-7x+6

Integral of x^2-7x+6 dx

The solution

You have entered [src]

  1                  
  /                  
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 |  / 2          \   
 |  \x  - 7*x + 6/ dx
 |                   
/                    
0

$$\int\limits_{0}^{1} \left(x^{2} - 7 x + 6\right)\, dx$$

Simplify

Detail solution

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:
  
  $\int \left(- 7 x\right)\, dx = - \int 7 x\, dx$
  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: $\frac{7 x^{2}}{2}$
  So, the result is: $- \frac{7 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 6\, dx = 6 x$
The result is: $\frac{x^{3}}{3} - \frac{7 x^{2}}{2} + 6 x$
Now simplify:

$\frac{x \left(2 x^{2} - 21 x + 36\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 21 x + 36\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 21 x + 36\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                  2    3
 | / 2          \                7*x    x 
 | \x  - 7*x + 6/ dx = C + 6*x - ---- + --
 |                                2     3 
/

$${{x^3}\over{3}}-{{7\,x^2}\over{2}}+6\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

17/6

$${{17}\over{6}}$$

17/6

$$\frac{17}{6}$$

Simplify

Numerical answer [src]

2.83333333333333

2.83333333333333

The graph

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

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Integral of x^2-7x+6 dx

Limits of integration:

The graph:

Piecewise:

The solution