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Similar expressions
3+x^2-1/(cos(x))
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What you mean?
(3 - x^2 - 1*1)/cos(x)
(3 - x^2 - 1*1)*x/cos(x)
3 - (x^2 - 1*1)/cos(x)
3 - (x^2 - 1*1)*x/cos(x)
3 - x*(2 - 1*1)/cos(x)
3 - x*(2 - 1*1)*x/cos(x)
3 - x^2 - x/cos(x)

You entered:

3-x^2-1/(cos(x))

What you mean?

(3 - x^2 - 1*1)/cos(x)

(3 - x^2 - 1*1)*x/cos(x)

3 - (x^2 - 1*1)/cos(x)

3 - (x^2 - 1*1)*x/cos(x)

3 - x*(2 - 1*1)/cos(x)

3 - x*(2 - 1*1)*x/cos(x)

3 - x^2 - x/cos(x)

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

The solution

You have entered [src]

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

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

Integral(3 - x^2 - 1/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:
  
  $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $- \frac{x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 3\, dx = 3 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{1}{\cos{\left(x \right)}}\right)\, dx = - \int \frac{1}{\cos{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}$
  So, the result is: $\frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}$
The result is: $- \frac{x^{3}}{3} + 3 x + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}$
Add the constant of integration:

$- \frac{x^{3}}{3} + 3 x + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}+ \mathrm{constant}$

The answer is:

$- \frac{x^{3}}{3} + 3 x + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$-{{\log \left(\sin x+1\right)}\over{2}}+{{\log \left(\sin x-1 \right)}\over{2}}-{{x^3}\over{3}}+3\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

8   log(1 - sin(1))   log(1 + sin(1))
- + --------------- - ---------------
3          2                 2

$$-{{3\,\log \left(\sin 1+1\right)-3\,\log \left(1-\sin 1\right)-16 }\over{6}}$$

8   log(1 - sin(1))   log(1 + sin(1))
- + --------------- - ---------------
3          2                 2

$$\frac{\log{\left(- \sin{\left(1 \right)} + 1 \right)}}{2} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{2} + \frac{8}{3}$$

Упростить

Numerical answer [src]

1.44047549578315

1.44047549578315

The graph

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

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You entered:

What you mean?

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

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Piecewise:

The solution