Integral of 2t⁵-8t³-8t³ dx

The solution

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 |  \2*t  - 8*t  - 8*t / dt
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$$\int\limits_{0}^{1} \left(- 8 t^{3} + \left(2 t^{5} - 8 t^{3}\right)\right)\, dt$$

Integral(2*t^5 - 8*t^3 - 8*t^3, (t, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 8 t^{3}\right)\, dt = - 8 \int t^{3}\, dt$
  1. The integral of $t^{n}$ is $\frac{t^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int t^{3}\, dt = \frac{t^{4}}{4}$
  So, the result is: $- 2 t^{4}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 t^{5}\, dt = 2 \int t^{5}\, dt$
    1. The integral of $t^{n}$ is $\frac{t^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int t^{5}\, dt = \frac{t^{6}}{6}$
    So, the result is: $\frac{t^{6}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 8 t^{3}\right)\, dt = - 8 \int t^{3}\, dt$
    1. The integral of $t^{n}$ is $\frac{t^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int t^{3}\, dt = \frac{t^{4}}{4}$
    So, the result is: $- 2 t^{4}$
  The result is: $\frac{t^{6}}{3} - 2 t^{4}$
The result is: $\frac{t^{6}}{3} - 4 t^{4}$
Now simplify:

$\frac{t^{4} \left(t^{2} - 12\right)}{3}$
Add the constant of integration:

$\frac{t^{4} \left(t^{2} - 12\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{t^{4} \left(t^{2} - 12\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | \2*t  - 8*t  - 8*t / dt = C - 4*t  + --
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$$\int \left(- 8 t^{3} + \left(2 t^{5} - 8 t^{3}\right)\right)\, dt = C + \frac{t^{6}}{3} - 4 t^{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-11/3

$$- \frac{11}{3}$$

-11/3

$$- \frac{11}{3}$$

-11/3

Numerical answer [src]

-3.66666666666667

-3.66666666666667

The graph

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

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Integral of 2t⁵-8t³-8t³ dx

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The solution