Integral of 1/3*x+1 dx

The solution

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 oo           
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 |  /x    \   
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$$\int\limits_{2}^{\infty} \left(\frac{x}{3} + 1\right)\, dx$$

Integral(x/3 + 1, (x, 2, oo))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{x}{3}\, dx = \frac{\int x\, dx}{3}$
  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: $\frac{x^{2}}{6}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{x^{2}}{6} + x$
Now simplify:

$\frac{x \left(x + 6\right)}{6}$
Add the constant of integration:

$\frac{x \left(x + 6\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x + 6\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                       2
 | /x    \              x 
 | |- + 1| dx = C + x + --
 | \3    /              6 
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$$\int \left(\frac{x}{3} + 1\right)\, dx = C + \frac{x^{2}}{6} + x$$

Simplify

The graph

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The answer [src]

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$$\infty$$

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$$\infty$$

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

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Integral of 1/3*x+1 dx

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