Integral of x^2+3x dx

The solution

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

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

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

Detail solution

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

$\frac{x^{2} \cdot \left(2 x + 9\right)}{6}$
Add the constant of integration:

$\frac{x^{2} \cdot \left(2 x + 9\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \cdot \left(2 x + 9\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{x^3}\over{3}}+{{3\,x^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

11/6

$${{11}\over{6}}$$

11/6

$$\frac{11}{6}$$

Упростить

Numerical answer [src]

1.83333333333333

1.83333333333333

The graph

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

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Integral of x^2+3x dx

Limits of integration:

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Piecewise:

The solution