Integral of 5+x dx

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

75/2

$$\frac{75}{2}$$

75/2

$$\frac{75}{2}$$

75/2

Numerical answer [src]

37.5

37.5

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