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Similar expressions
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Solving integrals/ (√x-1/cos^2x)

Integral of (√x-1/cos^2x) dx

The solution

You have entered [src]

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

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

2   sin(1)
- - ------
3   cos(1)

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

2   sin(1)
- - ------
3   cos(1)

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

2/3 - sin(1)/cos(1)

Numerical answer [src]

-0.890741057988236

-0.890741057988236

The graph

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

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Identical expressions

Similar expressions

Integral of (√x-1/cos^2x) dx

Limits of integration:

The graph:

Piecewise:

The solution