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Identical expressions
one /3x+ twenty
1 divide by 3x plus 20
one divide by 3x plus twenty
1 divide by 3x+20
1/3x+20dx
Similar expressions
1/3x-20

Integral of 1/3x+20 dx

The solution

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 15            
  /            
 |             
 |  /x     \   
 |  |- + 20| dx
 |  \3     /   
 |             
/              
0

$$\int\limits_{0}^{15} \left(\frac{x}{3} + 20\right)\, dx$$

Integral(x/3 + 20, (x, 0, 15))

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:
  
  $\int 20\, dx = 20 x$
The result is: $\frac{x^{2}}{6} + 20 x$
Now simplify:

$\frac{x \left(x + 120\right)}{6}$
Add the constant of integration:

$\frac{x \left(x + 120\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x + 120\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                           2
 | /x     \                 x 
 | |- + 20| dx = C + 20*x + --
 | \3     /                 6 
 |                            
/

$$\int \left(\frac{x}{3} + 20\right)\, dx = C + \frac{x^{2}}{6} + 20 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

675/2

$$\frac{675}{2}$$

675/2

$$\frac{675}{2}$$

675/2

Numerical answer [src]

337.5

337.5

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

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Identical expressions

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Integral of 1/3x+20 dx

Limits of integration:

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Piecewise:

The solution