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Identical expressions
3x^ two +4x- one
3x squared plus 4x minus 1
3x to the power of two plus 4x minus one
3x2+4x-1
3x²+4x-1
3x to the power of 2+4x-1
3x^2+4x-1dx
Similar expressions
3x^2+4x+1
3x^2-4x-1

Integral of 3x^2+4x-1 dx

The solution

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  9                    
  /                    
 |                     
 |  /   2          \   
 |  \3*x  + 4*x - 1/ dx
 |                     
/                      
4

$$\int\limits_{4}^{9} \left(\left(3 x^{2} + 4 x\right) - 1\right)\, dx$$

Integral(3*x^2 + 4*x - 1, (x, 4, 9))

Detail solution

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

$x \left(x^{2} + 2 x - 1\right)$
Add the constant of integration:

$x \left(x^{2} + 2 x - 1\right)+ \mathrm{constant}$

The answer is:

$x \left(x^{2} + 2 x - 1\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$790$$

Numerical answer [src]

790.0

790.0

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

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Integral of 3x^2+4x-1 dx

Limits of integration:

The graph:

Piecewise:

The solution