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Identical expressions
three *x³+4x
3 multiply by x³ plus 4x
three multiply by x³ plus 4x
3x³+4x
3*x³+4xdx
Similar expressions
3*x³-4x

Integral of 3*x³+4x dx

The solution

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

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

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x^{3}\, dx = 3 \int x^{3}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  So, the result is: $\frac{3 x^{4}}{4}$
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: $\frac{3 x^{4}}{4} + 2 x^{2}$
Now simplify:

$\frac{x^{2} \left(3 x^{2} + 8\right)}{4}$
Add the constant of integration:

$\frac{x^{2} \left(3 x^{2} + 8\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(3 x^{2} + 8\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

69/4

$$\frac{69}{4}$$

69/4

$$\frac{69}{4}$$

69/4

Numerical answer [src]

17.25

17.25

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

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Identical expressions

Similar expressions

Integral of 3*x³+4x dx

Limits of integration:

The graph:

Piecewise:

The solution