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Integral of d{x}:
Integral of 10x^4+30x^2–24x^5
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Integral of 4(2x-1)^2
Integral of cos(7x+2)
Identical expressions
10x^ four +30x^ two –24x^ five
10x to the power of 4 plus 30x squared –24x to the power of 5
10x to the power of four plus 30x to the power of two –24x to the power of five
10x4+30x2–24x5
10x⁴+30x²–24x⁵
10x to the power of 4+30x to the power of 2–24x to the power of 5
10x^4+30x^2–24x^5dx
Similar expressions
10x^4-30x^2–24x^5

Solving integrals/ 10x^4+30x^2–24x^5

Integral of 10x^4+30x^2–24x^5 dx

The solution

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  1                           
  /                           
 |                            
 |  /    4       2       5\   
 |  \10*x  + 30*x  - 24*x / dx
 |                            
/                             
0

$$\int\limits_{0}^{1} \left(- 24 x^{5} + 10 x^{4} + 30 x^{2}\right)\, dx$$

Integral(10*x^4 + 30*x^2 - 24*x^5, (x, 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:
  
  $\int \left(- 24 x^{5}\right)\, dx = - \int 24 x^{5}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 24 x^{5}\, dx = 24 \int x^{5}\, dx$
    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: $4 x^{6}$
  So, the result is: $- 4 x^{6}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 10 x^{4}\, dx = 10 \int x^{4}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{4}\, dx = \frac{x^{5}}{5}$
  So, the result is: $2 x^{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 30 x^{2}\, dx = 30 \int x^{2}\, dx$
  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: $10 x^{3}$
The result is: $- 4 x^{6} + 2 x^{5} + 10 x^{3}$
Now simplify:

$2 x^{3} \left(- 2 x^{3} + x^{2} + 5\right)$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                                    
 |                                                     
 | /    4       2       5\             6      5       3
 | \10*x  + 30*x  - 24*x / dx = C - 4*x  + 2*x  + 10*x 
 |                                                     
/

$$-4\,x^6+2\,x^5+10\,x^3$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$8$$

Simplify

Numerical answer [src]

8.0

8.0

The graph

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

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Integral of 10x^4+30x^2–24x^5 dx

Limits of integration:

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Piecewise:

The solution