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Integral of d{x}:
Integral of x^3*e^(x^4)
Integral of x*e^(4*x)
Integral of 1/(4+x^2)
Integral of x/sqrt(1+x^2)
Identical expressions
x^ three *e^(x^ four)
x cubed multiply by e to the power of (x to the power of 4)
x to the power of three multiply by e to the power of (x to the power of four)
x3*e(x4)
x3*ex4
x³*e^(x⁴)
x to the power of 3*e to the power of (x to the power of 4)
x^3e^(x^4)
x3e(x4)
x3ex4
x^3e^x^4
x^3*e^(x^4)dx

Solving integrals/ x^3*e^(x^4)

Integral of x^3*e^(x^4) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |      / 4\   
 |   3  \x /   
 |  x *E     dx
 |             
/              
0

$$\int\limits_{0}^{1} e^{x^{4}} x^{3}\, dx$$

Integral(x^3*E^(x^4), (x, 0, 1))

Detail solution

Let $u = x^{4}$ .

Then let $du = 4 x^{3} dx$ and substitute $\frac{du}{4}$ :

$\int \frac{e^{u}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $\frac{e^{u}}{4}$
Now substitute $u$ back in:

$\frac{e^{x^{4}}}{4}$
Add the constant of integration:

$\frac{e^{x^{4}}}{4}+ \mathrm{constant}$

The answer is:

$\frac{e^{x^{4}}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int e^{x^{4}} x^{3}\, dx = C + \frac{e^{x^{4}}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1   E
- - + -
  4   4

$$- \frac{1}{4} + \frac{e}{4}$$

  1   E
- - + -
  4   4

$$- \frac{1}{4} + \frac{e}{4}$$

-1/4 + E/4

Numerical answer [src]

0.429570457114761

0.429570457114761

The graph

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

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Identical expressions

Integral of x^3*e^(x^4) dx

Limits of integration:

The graph:

Piecewise:

The solution