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Identical expressions
5t^ two -2t- three
5t squared minus 2t minus 3
5t to the power of two minus 2t minus three
5t2-2t-3
5t²-2t-3
5t to the power of 2-2t-3
Similar expressions
5t^2+2t-3
5t^2-2t+3

Integral of 5t^2-2t-3 dt

The solution

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  5                    
  /                    
 |                     
 |  /   2          \   
 |  \5*t  - 2*t - 3/ dt
 |                     
/                      
2

$$\int\limits_{2}^{5} \left(\left(5 t^{2} - 2 t\right) - 3\right)\, dt$$

Integral(5*t^2 - 2*t - 3, (t, 2, 5))

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

$\frac{t \left(5 t^{2} - 3 t - 9\right)}{3}$
Add the constant of integration:

$\frac{t \left(5 t^{2} - 3 t - 9\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{t \left(5 t^{2} - 3 t - 9\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                         3
 | /   2          \           2         5*t 
 | \5*t  - 2*t - 3/ dt = C - t  - 3*t + ----
 |                                       3  
/

$$\int \left(\left(5 t^{2} - 2 t\right) - 3\right)\, dt = C + \frac{5 t^{3}}{3} - t^{2} - 3 t$$

Simplify

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Plot the graph f(x)

The answer [src]

$$165$$

Numerical answer [src]

165.0

165.0

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

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Integral of 5t^2-2t-3 dt

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Piecewise:

The solution