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Identical expressions
(2x- one)(3x+ four)
(2x minus 1)(3x plus 4)
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(2x-1)(3x+4)dx
Similar expressions
(2x+1)(3x+4)
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Solving integrals/ (2x-1)(3x+4)

Integral of (2x-1)(3x+4) dx

The solution

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  1                       
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 |  (2*x - 1)*(3*x + 4) dx
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0

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

Integral((2*x - 1)*(3*x + 4), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(2 x - 1\right) \left(3 x + 4\right) = 6 x^{2} + 5 x - 4$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 6 x^{2}\, dx = 6 \int x^{2}\, dx$
  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: $2 x^{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 x\, dx = 5 \int x\, dx$
  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: $\frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-4\right)\, dx = - 4 x$
The result is: $2 x^{3} + \frac{5 x^{2}}{2} - 4 x$
Now simplify:

$\frac{x \left(4 x^{2} + 5 x - 8\right)}{2}$
Add the constant of integration:

$\frac{x \left(4 x^{2} + 5 x - 8\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(4 x^{2} + 5 x - 8\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                             2
 |                                       3   5*x 
 | (2*x - 1)*(3*x + 4) dx = C - 4*x + 2*x  + ----
 |                                            2  
/

$$\int \left(2 x - 1\right) \left(3 x + 4\right)\, dx = C + 2 x^{3} + \frac{5 x^{2}}{2} - 4 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/2

$$\frac{1}{2}$$

1/2

$$\frac{1}{2}$$

1/2

Numerical answer [src]

0.5

0.5

The graph

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

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Integral of (2x-1)(3x+4) dx

Limits of integration:

The graph:

Piecewise:

The solution