Integral of x²+7x dx

The solution

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  1              
  /              
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 |  / 2      \   
 |  \x  + 7*x/ dx
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0

$$\int\limits_{0}^{1} \left(x^{2} + 7 x\right)\, dx$$

Integral(x^2 + 7*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:
  
  $\int 7 x\, dx = 7 \int x\, dx$
  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: $\frac{7 x^{2}}{2}$
The result is: $\frac{x^{3}}{3} + \frac{7 x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(2 x + 21\right)}{6}$
Add the constant of integration:

$\frac{x^{2} \left(2 x + 21\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 x + 21\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                      3      2
 | / 2      \          x    7*x 
 | \x  + 7*x/ dx = C + -- + ----
 |                     3     2  
/

$$\int \left(x^{2} + 7 x\right)\, dx = C + \frac{x^{3}}{3} + \frac{7 x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

23/6

$$\frac{23}{6}$$

23/6

$$\frac{23}{6}$$

23/6

Numerical answer [src]

3.83333333333333

3.83333333333333

The graph

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

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Identical expressions

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Integral of x²+7x dx

Limits of integration:

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Piecewise:

The solution