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Identical expressions
2x+ five /3x- one
2x plus 5 divide by 3x minus 1
2x plus five divide by 3x minus one
2x+5 divide by 3x-1
2x+5/3x-1dx
Similar expressions
2x-5/3x-1
2x+5/3x+1

Solving integrals/ 2x+5/3x-1

Integral of 2x+5/3x-1 dx

The solution

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  1                   
  /                   
 |                    
 |  /      5*x    \   
 |  |2*x + --- - 1| dx
 |  \       3     /   
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(\left(\frac{5 x}{3} + 2 x\right) - 1\right)\, dx$$

Integral(2*x + 5*x/3 - 1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{5 x}{3}\, dx = \frac{5 \int x\, dx}{3}$
    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: $\frac{5 x^{2}}{6}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x\, dx = 2 \int x\, dx$
    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: $x^{2}$
  The result is: $\frac{11 x^{2}}{6}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $\frac{11 x^{2}}{6} - x$
Now simplify:

$\frac{x \left(11 x - 6\right)}{6}$
Add the constant of integration:

$\frac{x \left(11 x - 6\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(11 x - 6\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                                  2
 | /      5*x    \              11*x 
 | |2*x + --- - 1| dx = C - x + -----
 | \       3     /                6  
 |                                   
/

$$\int \left(\left(\frac{5 x}{3} + 2 x\right) - 1\right)\, dx = C + \frac{11 x^{2}}{6} - x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/6

$$\frac{5}{6}$$

5/6

$$\frac{5}{6}$$

5/6

Numerical answer [src]

0.833333333333333

0.833333333333333

The graph

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

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Integral of 2x+5/3x-1 dx

Limits of integration:

The graph:

Piecewise:

The solution