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Identical expressions
(2e^ three +x)-3sec^2x
(2e cubed plus x) minus 3sec squared x
(2e to the power of three plus x) minus 3sec squared x
(2e3+x)-3sec2x
2e3+x-3sec2x
(2e³+x)-3sec²x
(2e to the power of 3+x)-3sec to the power of 2x
2e^3+x-3sec^2x
(2e^3+x)-3sec^2xdx
Similar expressions
(2e^3-x)-3sec^2x
(2e^3+x)+3sec^2x

Solving integrals/ (2e^3+x)-3sec^2x

Integral of (2e^3+x)-3sec^2x dx

The solution

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  1                          
  /                          
 |                           
 |  /   3            2   \   
 |  \2*e  + x - 3*sec (x)/ dx
 |                           
/                            
0

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

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

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 \sec^{2}{\left(x \right)}\right)\, dx = - \int 3 \sec^{2}{\left(x \right)}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 \sec^{2}{\left(x \right)}\, dx = 3 \int \sec^{2}{\left(x \right)}\, dx$
    1. $\int \sec^{2}{\left(x \right)}\, dx = \tan{\left(x \right)}$
    So, the result is: $3 \tan{\left(x \right)}$
  So, the result is: $- 3 \tan{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2 e^{3}\, dx = 2 x e^{3}$
The result is: $\frac{x^{2}}{2} + 2 x e^{3} - 3 \tan{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                                      
 |                                  2                    
 | /   3            2   \          x                    3
 | \2*e  + x - 3*sec (x)/ dx = C + -- - 3*tan(x) + 2*x*e 
 |                                 2                     
/

$$-3\,\tan x+{{x^2}\over{2}}+2\,e^3\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1      3   3*sin(1)
- + 2*e  - --------
2           cos(1)

$$-{{6\,\tan 1-4\,e^3-1}\over{2}}$$

1      3   3*sin(1)
- + 2*e  - --------
2           cos(1)

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

Упростить

Numerical answer [src]

35.9988506724106

35.9988506724106

The graph

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

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Integral of (2e^3+x)-3sec^2x dx

Limits of integration:

The graph:

Piecewise:

The solution