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

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  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
  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is .

      So, the result is:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                         
 |                                          
 | /     ___   4\                        3/2
 | |12*\/ x  - -| dx = C - 4*log(x) + 8*x   
 | \           x/                           
 |                                          
/                                           
$$\int \left(12 \sqrt{x} - \frac{4}{x}\right)\, dx = C + 8 x^{\frac{3}{2}} - 4 \log{\left(x \right)}$$
The graph
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.