Integral of a+x dx

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

Integral(a + x, (x, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The answer [src]

1/2 + a

$$a + \frac{1}{2}$$

1/2 + a

$$a + \frac{1}{2}$$

1/2 + a

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