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Integral of 3x^5-2x^3+5x^2-1
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Identical expressions
three x^ five - two x^3+5x^2- one
3x to the power of 5 minus 2x cubed plus 5x squared minus 1
three x to the power of five minus two x cubed plus 5x squared minus one
3x5-2x3+5x2-1
3x⁵-2x³+5x²-1
3x to the power of 5-2x to the power of 3+5x to the power of 2-1
3x^5-2x^3+5x^2-1dx
Similar expressions
3x^5+2x^3+5x^2-1
3x^5-2x^3+5x^2+1
3x^5-2x^3-5x^2-1

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

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

The solution

You have entered [src]

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

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

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

Detail solution

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

$\frac{x^{6}}{2} - \frac{x^{4}}{2} + \frac{5 x^{3}}{3} - x+ \mathrm{constant}$

The answer is:

$\frac{x^{6}}{2} - \frac{x^{4}}{2} + \frac{5 x^{3}}{3} - x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                    
 |                                    6        4      3
 | /   5      3      2    \          x        x    5*x 
 | \3*x  - 2*x  + 5*x  - 1/ dx = C + -- - x - -- + ----
 |                                   2        2     3  
/

$${{x^6}\over{2}}-{{x^4}\over{2}}+{{5\,x^3}\over{3}}-x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-68/3

$$-{{68}\over{3}}$$

-68/3

$$- \frac{68}{3}$$

Simplify

Numerical answer [src]

-22.6666666666667

-22.6666666666667

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution