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Similar expressions
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Integral of 2*cos(x)-sqrt(x)+4/x dx

The solution

You have entered [src]

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

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

Integral(2*cos(x) - sqrt(x) + 4/x, (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:
    
    $\int \left(- \sqrt{x}\right)\, dx = - \int \sqrt{x}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
    So, the result is: $- \frac{2 x^{\frac{3}{2}}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 \cos{\left(x \right)}\, dx = 2 \int \cos{\left(x \right)}\, dx$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
    So, the result is: $2 \sin{\left(x \right)}$
  The result is: $- \frac{2 x^{\frac{3}{2}}}{3} + 2 \sin{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{4}{x}\, dx = 4 \int \frac{1}{x}\, dx$
  1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
  So, the result is: $4 \log{\left(x \right)}$
The result is: $- \frac{2 x^{\frac{3}{2}}}{3} + 4 \log{\left(x \right)} + 2 \sin{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

177.378059838921

177.378059838921

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

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Identical expressions

Similar expressions

Integral of 2*cos(x)-sqrt(x)+4/x dx

Limits of integration:

The graph:

Piecewise:

The solution