Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^3*e^x
Integral of e^(a*x)
Integral of sin^4
Integral of -cos(x)
Identical expressions
5x^ three - two x^2- three
5x cubed minus 2x squared minus 3
5x to the power of three minus two x squared minus three
5x3-2x2-3
5x³-2x²-3
5x to the power of 3-2x to the power of 2-3
5x^3-2x^2-3dx
Similar expressions
5x^3-2x^2+3
5x^3+2x^2-3

Integral of 5x^3-2x^2-3 dx

The solution

You have entered [src]

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

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

Integral(5*x^3 - 2*x^2 - 3, (x, -1, 3))

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:
    
    $\int 5 x^{3}\, dx = 5 \int x^{3}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{3}\, dx = \frac{x^{4}}{4}$
    So, the result is: $\frac{5 x^{4}}{4}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 2 x^{2}\right)\, dx = - 2 \int x^{2}\, dx$
    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: $- \frac{2 x^{3}}{3}$
  The result is: $\frac{5 x^{4}}{4} - \frac{2 x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-3\right)\, dx = - 3 x$
The result is: $\frac{5 x^{4}}{4} - \frac{2 x^{3}}{3} - 3 x$
Now simplify:

$\frac{x \left(15 x^{3} - 8 x^{2} - 36\right)}{12}$
Add the constant of integration:

$\frac{x \left(15 x^{3} - 8 x^{2} - 36\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x \left(15 x^{3} - 8 x^{2} - 36\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            
 |                                     3      4
 | /   3      2    \                2*x    5*x 
 | \5*x  - 2*x  - 3/ dx = C - 3*x - ---- + ----
 |                                   3      4  
/

$$\int \left(\left(5 x^{3} - 2 x^{2}\right) - 3\right)\, dx = C + \frac{5 x^{4}}{4} - \frac{2 x^{3}}{3} - 3 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

208/3

$$\frac{208}{3}$$

208/3

$$\frac{208}{3}$$

208/3

Numerical answer [src]

69.3333333333333

69.3333333333333

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 5x^3-2x^2-3 dx

Limits of integration:

The graph:

Piecewise:

The solution