Integral of (x+1)/5 dx

The solution

You have entered [src]

  1         
  /         
 |          
 |  x + 1   
 |  ----- dx
 |    5     
 |          
/           
0

$$\int\limits_{0}^{1} \frac{x + 1}{5}\, dx$$

Integral((x + 1)/5, (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{x + 1}{5}\, dx = \frac{\int \left(x + 1\right)\, dx}{5}$
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, dx = x$
  The result is: $\frac{x^{2}}{2} + x$
So, the result is: $\frac{x^{2}}{10} + \frac{x}{5}$
Now simplify:

$\frac{x \left(x + 2\right)}{10}$
Add the constant of integration:

$\frac{x \left(x + 2\right)}{10}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x + 2\right)}{10}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                     
 |                     2
 | x + 1          x   x 
 | ----- dx = C + - + --
 |   5            5   10
 |                      
/

$$\int \frac{x + 1}{5}\, dx = C + \frac{x^{2}}{10} + \frac{x}{5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/10

$$\frac{3}{10}$$

3/10

$$\frac{3}{10}$$

3/10

Numerical answer [src]

0.3

0.3

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x+1)/5 dx

Limits of integration:

The graph:

Piecewise:

The solution