Integral of 3x²+2x³ dx

The solution

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

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

Integral(3*x^2 + 2*x^3, (x, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/2

$$\frac{3}{2}$$

3/2

$$\frac{3}{2}$$

3/2

Numerical answer [src]

1.5

1.5

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

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Integral of 3x²+2x³ dx

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The solution