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Identical expressions
(one /cos^2x-3x+ four)
(1 divide by co sinus of e of squared x minus 3x plus 4)
(one divide by co sinus of e of squared x minus 3x plus four)
(1/cos2x-3x+4)
1/cos2x-3x+4
(1/cos²x-3x+4)
(1/cos to the power of 2x-3x+4)
1/cos^2x-3x+4
(1 divide by cos^2x-3x+4)
(1/cos^2x-3x+4)dx
Similar expressions
(1/cos^2x+3x+4)
(1/cos^2x-3x-4)

Integral of (1/cos^2x-3x+4) dx

The solution

You have entered [src]

  1                       
  /                       
 |                        
 |  /   1             \   
 |  |------- - 3*x + 4| dx
 |  |   2             |   
 |  \cos (x)          /   
 |                        
/                         
0

$$\int\limits_{0}^{1} \left(\left(- 3 x + \frac{1}{\cos^{2}{\left(x \right)}}\right) + 4\right)\, dx$$

Integral(1/(cos(x)^2) - 3*x + 4, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 3 x\right)\, dx = - 3 \int x\, dx$
    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: $- \frac{3 x^{2}}{2}$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
  The result is: $- \frac{3 x^{2}}{2} + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
The result is: $- \frac{3 x^{2}}{2} + 4 x + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
Now simplify:

$- \frac{3 x^{2}}{2} + 4 x + \tan{\left(x \right)}$
Add the constant of integration:

$- \frac{3 x^{2}}{2} + 4 x + \tan{\left(x \right)}+ \mathrm{constant}$

The answer is:

$- \frac{3 x^{2}}{2} + 4 x + \tan{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                                       2         
 | /   1             \                3*x    sin(x)
 | |------- - 3*x + 4| dx = C + 4*x - ---- + ------
 | |   2             |                 2     cos(x)
 | \cos (x)          /                             
 |                                                 
/

$$\int \left(\left(- 3 x + \frac{1}{\cos^{2}{\left(x \right)}}\right) + 4\right)\, dx = C - \frac{3 x^{2}}{2} + 4 x + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

5   sin(1)
- + ------
2   cos(1)

$$\frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + \frac{5}{2}$$

5   sin(1)
- + ------
2   cos(1)

$$\frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + \frac{5}{2}$$

5/2 + sin(1)/cos(1)

Numerical answer [src]

4.0574077246549

4.0574077246549

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

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Identical expressions

Similar expressions

Integral of (1/cos^2x-3x+4) dx

Limits of integration:

The graph:

Piecewise:

The solution