Mister Exam

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Integral of d{x}:
Integral of xe^(x^2)
Integral of x^2*y
Integral of sin^2
Integral of exp(2*x)
Identical expressions
x*e^3x^ two + two
x multiply by e cubed x squared plus 2
x multiply by e cubed x to the power of two plus two
x*e3x2+2
x*e³x²+2
x*e to the power of 3x to the power of 2+2
xe^3x^2+2
xe3x2+2
x*e^3x^2+2dx
Similar expressions
x*e^3x^2-2
What you mean?
x*e^3*x^2 + 2
x*e^((3*x)^2) + 2
x*e^((3*x)^2) + 2

You entered:

x*e^3x^2+2

What you mean?

x*e^3*x^2 + 2

x*e^((3*x)^2) + 2

x*e^((3*x)^2) + 2

Integral of x*e^3x^2+2 dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |  /   3  2    \   
 |  \x*E *x  + 2/ dx
 |                  
/                   
0

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

Integral((x*E^3)*x^2 + 2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Let $u = x^{2}$ .
  
  Then let $du = 2 x dx$ and substitute $\frac{du e^{3}}{2}$ :
  
  $\int \frac{u e^{3}}{2}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u\, du = \frac{e^{3} \int u\, du}{2}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
    So, the result is: $\frac{u^{2} e^{3}}{4}$
  Now substitute $u$ back in:
  
  $\frac{x^{4} e^{3}}{4}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2\, dx = 2 x$
The result is: $\frac{x^{4} e^{3}}{4} + 2 x$
Now simplify:

$\frac{x \left(x^{3} e^{3} + 8\right)}{4}$
Add the constant of integration:

$\frac{x \left(x^{3} e^{3} + 8\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} e^{3} + 8\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$2 + \frac{e^{3}}{4}$$

$$2 + \frac{e^{3}}{4}$$

2 + exp(3)/4

Numerical answer [src]

7.02138423079692

7.02138423079692

The graph

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

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Identical expressions

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You entered:

What you mean?

Integral of x*e^3x^2+2 dx

Limits of integration:

The graph:

Piecewise:

The solution