Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^(2*x+1)
Integral of e^x²
Integral of (-x)/(1+x^2)
Integral of sqrt(x^2+4)/x^2
Identical expressions
3sqrtx-(x+ two)
3 square root of x minus (x plus 2)
3 square root of x minus (x plus two)
3√x-(x+2)
3sqrtx-x+2
3sqrtx-(x+2)dx
Similar expressions
3sqrtx+(x+2)
3sqrtx-(x-2)

Solving integrals/ 3sqrtx-(x+2)

Integral of 3sqrtx-(x+2) dx

The solution

You have entered [src]

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

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

Integral(3*sqrt(x) - (x + 2), (x, -1, 4))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 \sqrt{x}\, dx = 3 \int \sqrt{x}\, dx$
  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: $2 x^{\frac{3}{2}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- (x + 2)\right)\, dx = - \int \left(x + 2\right)\, dx$
  1. Integrate term-by-term:
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 2\, dx = 2 x$
    The result is: $\frac{x^{2}}{2} + 2 x$
  So, the result is: $- \frac{x^{2}}{2} - 2 x$
The result is: $2 x^{\frac{3}{2}} - \frac{x^{2}}{2} - 2 x$
Add the constant of integration:

$2 x^{\frac{3}{2}} - \frac{x^{2}}{2} - 2 x+ \mathrm{constant}$

The answer is:

$2 x^{\frac{3}{2}} - \frac{x^{2}}{2} - 2 x+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$-{{x^2}\over{2}}+2\,x^{{{3}\over{2}}}-2\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-3/2 + 2*I

$${{4\,i-3}\over{2}}$$

-3/2 + 2*I

$$- \frac{3}{2} + 2 i$$

Упростить

Numerical answer [src]

(-1.4977217544493 + 2.00061352543914j)

(-1.4977217544493 + 2.00061352543914j)

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 3sqrtx-(x+2) dx

Limits of integration:

The graph:

Piecewise:

The solution