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Identical expressions
seven /8x²+ one /5x- twenty
7 divide by 8x² plus 1 divide by 5x minus 20
seven divide by 8x² plus one divide by 5x minus twenty
7 divide by 8x²+1 divide by 5x-20
7/8x²+1/5x-20dx
Similar expressions
7/8x²+1/5x+20
7/8x²-1/5x-20

Integral of 7/8x²+1/5x-20 dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  /   2         \   
 |  |7*x    x     |   
 |  |---- + - - 20| dx
 |  \ 8     5     /   
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(\left(\frac{7 x^{2}}{8} + \frac{x}{5}\right) - 20\right)\, dx$$

Integral(7*x^2/8 + x/5 - 20, (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:
    
    $\int \frac{7 x^{2}}{8}\, dx = \frac{7 \int x^{2}\, dx}{8}$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $\frac{7 x^{3}}{24}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{x}{5}\, dx = \frac{\int x\, dx}{5}$
    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: $\frac{x^{2}}{10}$
  The result is: $\frac{7 x^{3}}{24} + \frac{x^{2}}{10}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-20\right)\, dx = - 20 x$
The result is: $\frac{7 x^{3}}{24} + \frac{x^{2}}{10} - 20 x$
Now simplify:

$\frac{x \left(35 x^{2} + 12 x - 2400\right)}{120}$
Add the constant of integration:

$\frac{x \left(35 x^{2} + 12 x - 2400\right)}{120}+ \mathrm{constant}$

The answer is:

$\frac{x \left(35 x^{2} + 12 x - 2400\right)}{120}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                          
 | /   2         \                  2      3
 | |7*x    x     |                 x    7*x 
 | |---- + - - 20| dx = C - 20*x + -- + ----
 | \ 8     5     /                 10    24 
 |                                          
/

$$\int \left(\left(\frac{7 x^{2}}{8} + \frac{x}{5}\right) - 20\right)\, dx = C + \frac{7 x^{3}}{24} + \frac{x^{2}}{10} - 20 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2353 
------
 120

$$- \frac{2353}{120}$$

-2353 
------
 120

$$- \frac{2353}{120}$$

-2353/120

Numerical answer [src]

-19.6083333333333

-19.6083333333333

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

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Integral of 7/8x²+1/5x-20 dx

Limits of integration:

The graph:

Piecewise:

The solution