Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^x/(1+e^x)
Integral of sin^2(3x)
Integral of sin(x)/cos(x)
Integral of |-1+x|
Identical expressions
8x^ seven +x^ five -3x^ two +4dx
8x to the power of 7 plus x to the power of 5 minus 3x squared plus 4dx
8x to the power of seven plus x to the power of five minus 3x to the power of two plus 4dx
8x7+x5-3x2+4dx
8x⁷+x⁵-3x²+4dx
8x to the power of 7+x to the power of 5-3x to the power of 2+4dx
Similar expressions
8x^7-x^5-3x^2+4dx
8x^7+x^5+3x^2+4dx
8x^7+x^5-3x^2-4dx

Solving integrals/ 8x^7+x^5-3x^2+4dx

Integral of 8x^7+x^5-3x^2+4dx dx

The solution

You have entered [src]

  1                            
  /                            
 |                             
 |  /   7    5      2      \   
 |  \8*x  + x  - 3*x  + 4*1/ dx
 |                             
/                              
0

$$\int\limits_{0}^{1} \left(8 x^{7} + x^{5} - 3 x^{2} + 4 \cdot 1\right)\, dx$$

Integral(8*x^7 + x^5 - 3*x^2 + 4*1, (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:
  
  $\int 8 x^{7}\, dx = 8 \int x^{7}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{7}\, dx = \frac{x^{8}}{8}$
  So, the result is: $x^{8}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{5}\, dx = \frac{x^{6}}{6}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 x^{2}\right)\, dx = - \int 3 x^{2}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
    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: $x^{3}$
  So, the result is: $- x^{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4 \cdot 1\, dx = 4 x$
The result is: $x^{8} + \frac{x^{6}}{6} - x^{3} + 4 x$
Now simplify:

$x \left(x^{7} + \frac{x^{5}}{6} - x^{2} + 4\right)$
Add the constant of integration:

$x \left(x^{7} + \frac{x^{5}}{6} - x^{2} + 4\right)+ \mathrm{constant}$

The answer is:

$x \left(x^{7} + \frac{x^{5}}{6} - x^{2} + 4\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                    
 |                                                    6
 | /   7    5      2      \           8    3         x 
 | \8*x  + x  - 3*x  + 4*1/ dx = C + x  - x  + 4*x + --
 |                                                   6 
/

$$x^8+{{x^6}\over{6}}-x^3+4\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

25/6

$${{25}\over{6}}$$

25/6

$$\frac{25}{6}$$

Simplify

Numerical answer [src]

4.16666666666667

4.16666666666667

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 8x^7+x^5-3x^2+4dx dx

Limits of integration:

The graph:

Piecewise:

The solution