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Identical expressions
4e^x-4cosx
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Similar expressions
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Solving integrals/ 4e^x-4cosx

Integral of 4e^x-4cosx dx

The solution

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  1                     
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 |  /   x           \   
 |  \4*e  - 4*cos(x)/ dx
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0

$$\int\limits_{0}^{1} \left(4 e^{x} - 4 \cos{\left(x \right)}\right)\, dx$$

Integral(4*E^x - 4*cos(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:
  
  $\int 4 e^{x}\, dx = 4 \int e^{x}\, dx$
  1. The integral of the exponential function is itself.
    
    $\int e^{x}\, dx = e^{x}$
  So, the result is: $4 e^{x}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 \cos{\left(x \right)}\right)\, dx = - \int 4 \cos{\left(x \right)}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 4 \cos{\left(x \right)}\, dx = 4 \int \cos{\left(x \right)}\, dx$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
    So, the result is: $4 \sin{\left(x \right)}$
  So, the result is: $- 4 \sin{\left(x \right)}$
The result is: $4 e^{x} - 4 \sin{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                          
 |                                           
 | /   x           \                        x
 | \4*e  - 4*cos(x)/ dx = C - 4*sin(x) + 4*e 
 |                                           
/

$$4\,e^{x}-4\,\sin x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-4 - 4*sin(1) + 4*e

$$-4\,\sin 1+4\,e-4$$

-4 - 4*sin(1) + 4*e

$$-4 - 4 \sin{\left(1 \right)} + 4 e$$

Упростить

Numerical answer [src]

3.50724337460459

3.50724337460459

The graph

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

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Identical expressions

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Integral of 4e^x-4cosx dx

Limits of integration:

The graph:

Piecewise:

The solution