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Integral of d{x}:
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Graphing y =:
x^3+3*x^2
Derivative of:
x^3+3*x^2
Limit of the function:
x^3+3*x^2
Identical expressions
x^ three + three *x^ two
x cubed plus 3 multiply by x squared
x to the power of three plus three multiply by x to the power of two
x3+3*x2
x³+3*x²
x to the power of 3+3*x to the power of 2
x^3+3x^2
x3+3x2
x^3+3*x^2dx
Similar expressions
((1/(x^3))+(3x^2)-4)dx
(x^3+3x^2)/32
x^3-3*x^2
(x^3+3x^2+4x)/x

Integral of x^3+3*x^2 dx

The solution

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

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$8$$

Numerical answer [src]

8.0

8.0

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

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Integral of x^3+3*x^2 dx

Limits of integration:

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Piecewise:

The solution