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Integral of d{x}:
Integral of x/(x+1)
Integral of -e^-x
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Integral of log(x)*dx/x
Identical expressions
three *x^ two - four /x^(x^ three)+x
3 multiply by x squared minus 4 divide by x to the power of (x cubed ) plus x
three multiply by x to the power of two minus four divide by x to the power of (x to the power of three) plus x
3*x2-4/x(x3)+x
3*x2-4/xx3+x
3*x²-4/x^(x³)+x
3*x to the power of 2-4/x to the power of (x to the power of 3)+x
3x^2-4/x^(x^3)+x
3x2-4/x(x3)+x
3x2-4/xx3+x
3x^2-4/x^x^3+x
3*x^2-4 divide by x^(x^3)+x
3*x^2-4/x^(x^3)+xdx
Similar expressions
3*x^2+4/x^(x^3)+x
3*x^2-4/x^(x^3)-x
What you mean?
(3*x^2 - 1*4)/(x^(x^3) + x)
(3*x^2 - 1*4)/(x^(x^3)) + x
(3*x^2 - 1*4)/((x^x*3)) + x
(3*x^2 - 1*4)/(x^(x^3)) + x
(3*x^2 - 1*4)*x^3/x + x
(3*x^2 - 1*4)/(x^(x^3)) + x
3*x^2 - 4/(x^(x^3)) + x

You entered:

3*x^2-4/x^(x^3)+x

What you mean?

(3*x^2 - 1*4)/(x^(x^3) + x)

(3*x^2 - 1*4)/(x^(x^3)) + x

(3*x^2 - 1*4)/((x^x*3)) + x

(3*x^2 - 1*4)/(x^(x^3)) + x

(3*x^2 - 1*4)*x^3/x + x

(3*x^2 - 1*4)/(x^(x^3)) + x

3*x^2 - 4/(x^(x^3)) + x

Integral of 3*x^2-4/x^(x^3)+x dx

The solution

You have entered [src]

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

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

Integral(3*x^2 - 4/(x^(x^3)) + x, (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:
  
  $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
  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: $x^{3}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{4}{x^{x^{3}}}\right)\, dx = - \int \frac{4}{x^{x^{3}}}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{4}{x^{x^{3}}}\, dx = 4 \int \frac{1}{x^{x^{3}}}\, dx$
    1. Don't know the steps in finding this integral.
      
      But the integral is
      
      $\int x^{- x^{3}}\, dx$
    So, the result is: $4 \int x^{- x^{3}}\, dx$
  So, the result is: $- 4 \int x^{- x^{3}}\, dx$
The result is: $x^{3} + \frac{x^{2}}{2} - 4 \int x^{- x^{3}}\, dx$
Add the constant of integration:

$x^{3} + \frac{x^{2}}{2} - 4 \int x^{- x^{3}}\, dx+ \mathrm{constant}$

The answer is:

$x^{3} + \frac{x^{2}}{2} - 4 \int x^{- x^{3}}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

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

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

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

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

Упростить

Numerical answer [src]

-2.7620728237106

-2.7620728237106

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

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What you mean?

Integral of 3*x^2-4/x^(x^3)+x dx

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The solution