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Identical expressions
four *3sqrt(x)- four /x
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Similar expressions
4*3sqrt(x)+4/x

Integral of 4*3sqrt(x)-4/x dx

The solution

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  1                  
  /                  
 |                   
 |  /     ___   4\   
 |  |12*\/ x  - -| dx
 |  \           x/   
 |                   
/                    
0

$$\int\limits_{0}^{1} \left(12 \sqrt{x} - \frac{4}{x}\right)\, dx$$

Integral(12*sqrt(x) - 4/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:
  
  $\int 12 \sqrt{x}\, dx = 12 \int \sqrt{x}\, dx$
  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: $8 x^{\frac{3}{2}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{4}{x}\right)\, dx = - 4 \int \frac{1}{x}\, dx$
  1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
  So, the result is: $- 4 \log{\left(x \right)}$
The result is: $8 x^{\frac{3}{2}} - 4 \log{\left(x \right)}$
Add the constant of integration:

$8 x^{\frac{3}{2}} - 4 \log{\left(x \right)}+ \mathrm{constant}$

The answer is:

$8 x^{\frac{3}{2}} - 4 \log{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                          
 | /     ___   4\                        3/2
 | |12*\/ x  - -| dx = C - 4*log(x) + 8*x   
 | \           x/                           
 |                                          
/

$$\int \left(12 \sqrt{x} - \frac{4}{x}\right)\, dx = C + 8 x^{\frac{3}{2}} - 4 \log{\left(x \right)}$$

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]

-168.361784535972

-168.361784535972

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

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Integral of 4*3sqrt(x)-4/x dx

Limits of integration:

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Piecewise:

The solution