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Integral of d{x}:
Integral of e^3x
Integral of sinx/cos2x
Integral of -e^x
Integral of sqrt(x^2+1)/x^3
Identical expressions
(e^3x- two cosx/2)
(e cubed x minus 2 co sinus of e of x divide by 2)
(e cubed x minus two co sinus of e of x divide by 2)
(e3x-2cosx/2)
e3x-2cosx/2
(e³x-2cosx/2)
(e to the power of 3x-2cosx/2)
e^3x-2cosx/2
(e^3x-2cosx divide by 2)
(e^3x-2cosx/2)dx
Similar expressions
(e^3x+2cosx/2)

Integral of (e^3x-2cosx/2) dx

The solution

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  1                     
  /                     
 |                      
 |  / 3     2*cos(x)\   
 |  |E *x - --------| dx
 |  \          2    /   
 |                      
/                       
0

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

Integral(E^3*x - 2*cos(x)/2, (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:
  
  $\int e^{3} x\, dx = e^{3} \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{x^{2} e^{3}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{2 \cos{\left(x \right)}}{2}\right)\, dx = - \frac{\int 2 \cos{\left(x \right)}\, dx}{2}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 \cos{\left(x \right)}\, dx = 2 \int \cos{\left(x \right)}\, dx$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
    So, the result is: $2 \sin{\left(x \right)}$
  So, the result is: $- \sin{\left(x \right)}$
The result is: $\frac{x^{2} e^{3}}{2} - \sin{\left(x \right)}$
Add the constant of integration:

$\frac{x^{2} e^{3}}{2} - \sin{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} e^{3}}{2} - \sin{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                      2  3
 | / 3     2*cos(x)\                   x *e 
 | |E *x - --------| dx = C - sin(x) + -----
 | \          2    /                     2  
 |                                          
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

 3         
e          
-- - sin(1)
2

$$- \sin{\left(1 \right)} + \frac{e^{3}}{2}$$

 3         
e          
-- - sin(1)
2

$$- \sin{\left(1 \right)} + \frac{e^{3}}{2}$$

exp(3)/2 - sin(1)

Numerical answer [src]

9.20129747678594

9.20129747678594

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

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Identical expressions

Similar expressions

Integral of (e^3x-2cosx/2) dx

Limits of integration:

The graph:

Piecewise:

The solution