Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sinx
Integral of cosx^2
Integral of sinh(x)
Integral of xcos(nx)
Identical expressions
two *exp(x)-exp(two *x)
2 multiply by exponent of (x) minus exponent of (2 multiply by x)
two multiply by exponent of (x) minus exponent of (two multiply by x)
2exp(x)-exp(2x)
2expx-exp2x
2*exp(x)-exp(2*x)dx
Similar expressions
2*exp(x)+exp(2*x)

Solving integrals/ 2*exp(x)-exp(2*x)

Integral of 2exp(x)-exp(2x) dx

The solution

You have entered [src]

 log(2)                
    /                  
   |                   
   |   /   x    2*x\   
   |   \2*e  - e   / dx
   |                   
  /                    
  0

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

Integral(2*exp(x) - exp(2*x), (x, 0, log(2)))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- e^{2 x}\right)\, dx = - \int e^{2 x}\, dx$
  1. There are multiple ways to do this integral.
    Method #1
    1. Let $u = 2 x$ .
      
      Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :
      
      $\int \frac{e^{u}}{4}\, du$
      
      The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{e^{u}}{2}\, du = \frac{\int e^{u}\, du}{2}$
      
      The integral of the exponential function is itself.
      
      $\int e^{u}\, du = e^{u}$
      
      So, the result is: $\frac{e^{u}}{2}$
      
      Now substitute $u$ back in:
      
      $\frac{e^{2 x}}{2}$
    Method #2
    1. Let $u = e^{2 x}$ .
      
      Then let $du = 2 e^{2 x} dx$ and substitute $\frac{du}{2}$ :
      
      $\int \frac{1}{4}\, du$
      
      The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{1}{2}\, du = \frac{\int 1\, du}{2}$
      
      The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
      
      So, the result is: $\frac{u}{2}$
      
      Now substitute $u$ back in:
      
      $\frac{e^{2 x}}{2}$
  So, the result is: $- \frac{e^{2 x}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 e^{x}\, dx = 2 \int e^{x}\, dx$
  1. The integral of the exponential function is itself.
    
    $\int e^{x}\, dx = e^{x}$
  So, the result is: $2 e^{x}$
The result is: $- \frac{e^{2 x}}{2} + 2 e^{x}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$$2\,e^{x}-{{e^{2\,x}}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/2

$${{1}\over{2}}$$

1/2

$$\frac{1}{2}$$

Simplify

Numerical answer [src]

0.5

0.5

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 2exp(x)-exp(2x) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 2*exp(x)-exp(2*x) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2

Integral of 2exp(x)-exp(2x) dx