Integral of x^4+x dx

You have entered [src]

  2            
  /            
 |             
 |  / 4    \   
 |  \x  + x/ dx
 |             
/              
0

$$\int\limits_{0}^{2} \left(x^{4} + x\right)\, dx$$

Integral(x^4 + x, (x, 0, 2))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{4}\, dx = \frac{x^{5}}{5}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
The result is: $\frac{x^{5}}{5} + \frac{x^{2}}{2}$
Add the constant of integration:

$\frac{x^{5}}{5} + \frac{x^{2}}{2}+ \mathrm{constant}$

The answer is:

$\frac{x^{5}}{5} + \frac{x^{2}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                    2    5
 | / 4    \          x    x 
 | \x  + x/ dx = C + -- + --
 |                   2    5 
/

$$\int \left(x^{4} + x\right)\, dx = C + \frac{x^{5}}{5} + \frac{x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

42/5

$$\frac{42}{5}$$

42/5

$$\frac{42}{5}$$

42/5

Numerical answer [src]

8.4

8.4

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