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Identical expressions
(x^ two +4x- one)dx
(x squared plus 4x minus 1)dx
(x to the power of two plus 4x minus one)dx
(x2+4x-1)dx
x2+4x-1dx
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Similar expressions
(x^2+4x+1)dx
(x^2-4x-1)dx

Solving integrals/ (x^2+4x-1)dx

Integral of (x^2+4x-1)dx dx

The solution

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  3                  
  /                  
 |                   
 |  / 2          \   
 |  \x  + 4*x - 1/ dx
 |                   
/                    
0

$$\int\limits_{0}^{3} \left(\left(x^{2} + 4 x\right) - 1\right)\, dx$$

Integral(x^2 + 4*x - 1, (x, 0, 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:
    
    $\int 4 x\, dx = 4 \int x\, dx$
    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: $2 x^{2}$
  The result is: $\frac{x^{3}}{3} + 2 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $\frac{x^{3}}{3} + 2 x^{2} - x$
Now simplify:

$\frac{x \left(x^{2} + 6 x - 3\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 6 x - 3\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 6 x - 3\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                     3
 | / 2          \                 2   x 
 | \x  + 4*x - 1/ dx = C - x + 2*x  + --
 |                                    3 
/

$$\int \left(\left(x^{2} + 4 x\right) - 1\right)\, dx = C + \frac{x^{3}}{3} + 2 x^{2} - x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$24$$

Numerical answer [src]

24.0

24.0

The graph

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

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Integral of (x^2+4x-1)dx dx

Limits of integration:

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Piecewise:

The solution