Mister Exam

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Integral of d{x}:
Integral of 1/(2+x^2)
Integral of x^2*lnx
Integral of x(x-1)(x-2)
Integral of x^4*e^(x^5)
Identical expressions
x^ four *e^(x^ five)
x to the power of 4 multiply by e to the power of (x to the power of 5)
x to the power of four multiply by e to the power of (x to the power of five)
x4*e(x5)
x4*ex5
x⁴*e^(x⁵)
x^4e^(x^5)
x4e(x5)
x4ex5
x^4e^x^5
x^4*e^(x^5)dx

Solving integrals/ x^4*e^(x^5)

Integral of x^4*e^(x^5) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |      / 5\   
 |   4  \x /   
 |  x *E     dx
 |             
/              
0

$$\int\limits_{0}^{1} e^{x^{5}} x^{4}\, dx$$

Integral(x^4*E^(x^5), (x, 0, 1))

Detail solution

Let $u = x^{5}$ .

Then let $du = 5 x^{4} dx$ and substitute $\frac{du}{5}$ :

$\int \frac{e^{u}}{5}\, du$
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: $\frac{e^{u}}{5}$
Now substitute $u$ back in:

$\frac{e^{x^{5}}}{5}$
Add the constant of integration:

$\frac{e^{x^{5}}}{5}+ \mathrm{constant}$

The answer is:

$\frac{e^{x^{5}}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                    / 5\
 |     / 5\           \x /
 |  4  \x /          e    
 | x *E     dx = C + -----
 |                     5  
/

$$\int e^{x^{5}} x^{4}\, dx = C + \frac{e^{x^{5}}}{5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1   E
- - + -
  5   5

$$- \frac{1}{5} + \frac{e}{5}$$

  1   E
- - + -
  5   5

$$- \frac{1}{5} + \frac{e}{5}$$

-1/5 + E/5

Numerical answer [src]

0.343656365691809

0.343656365691809

The graph

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

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Identical expressions

Integral of x^4*e^(x^5) dx

Limits of integration:

The graph:

Piecewise:

The solution