Integral of 5*x+1 dx

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$$\int\limits_{0}^{1} \left(5 x + 1\right)\, dx$$

Integral(5*x + 1, (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:
  
  $\int 5 x\, dx = 5 \int x\, dx$
  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: $\frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{5 x^{2}}{2} + x$
Now simplify:

$\frac{x \left(5 x + 2\right)}{2}$
Add the constant of integration:

$\frac{x \left(5 x + 2\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(5 x + 2\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          2
 |                        5*x 
 | (5*x + 1) dx = C + x + ----
 |                         2  
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$$\int \left(5 x + 1\right)\, dx = C + \frac{5 x^{2}}{2} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

7/2

$$\frac{7}{2}$$

7/2

$$\frac{7}{2}$$

7/2

Numerical answer [src]

3.5

3.5

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