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Identical expressions
(3x^ two)-(four *sqrtx)+ one /x
(3x squared ) minus (4 multiply by square root of x) plus 1 divide by x
(3x to the power of two) minus (four multiply by square root of x) plus one divide by x
(3x^2)-(4*√x)+1/x
(3x2)-(4*sqrtx)+1/x
3x2-4*sqrtx+1/x
(3x²)-(4*sqrtx)+1/x
(3x to the power of 2)-(4*sqrtx)+1/x
(3x^2)-(4sqrtx)+1/x
(3x2)-(4sqrtx)+1/x
3x2-4sqrtx+1/x
3x^2-4sqrtx+1/x
(3x^2)-(4*sqrtx)+1 divide by x
(3x^2)-(4*sqrtx)+1/xdx
Similar expressions
(3x^2)-(4*sqrtx)-1/x
(3x^2)+(4*sqrtx)+1/x

Integral of (3x^2)-(4*sqrtx)+1/x dx

The solution

You have entered [src]

  1                        
  /                        
 |                         
 |  /   2       ___   1\   
 |  |3*x  - 4*\/ x  + -| dx
 |  \                 x/   
 |                         
/                          
0

$$\int\limits_{0}^{1} \left(\left(- 4 \sqrt{x} + 3 x^{2}\right) + \frac{1}{x}\right)\, dx$$

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                                  
 |                                       3/2         
 | /   2       ___   1\           3   8*x            
 | |3*x  - 4*\/ x  + -| dx = C + x  - ------ + log(x)
 | \                 x/                 3            
 |                                                   
/

$$\int \left(\left(- 4 \sqrt{x} + 3 x^{2}\right) + \frac{1}{x}\right)\, dx = C - \frac{8 x^{\frac{3}{2}}}{3} + x^{3} + \log{\left(x \right)}$$

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]

42.4237794673262

42.4237794673262

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

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Identical expressions

Similar expressions

Integral of (3x^2)-(4*sqrtx)+1/x dx

Limits of integration:

The graph:

Piecewise:

The solution