Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 2/x^4
Integral of sin(5x)
Integral of 1/xdx
Integral of e^(3*x)/3
Identical expressions
(x-(two *y)+ six)+(three *(sqrt(x)))
(x minus (2 multiply by y) plus 6) plus (3 multiply by ( square root of (x)))
(x minus (two multiply by y) plus six) plus (three multiply by ( square root of (x)))
(x-(2*y)+6)+(3*(√(x)))
(x-(2y)+6)+(3(sqrt(x)))
x-2y+6+3sqrtx
(x-(2*y)+6)+(3*(sqrt(x)))dx
Similar expressions
(x-(2*y)+6)-(3*(sqrt(x)))
(x-(2*y)-6)+(3*(sqrt(x)))
(x+(2*y)+6)+(3*(sqrt(x)))

Solving integrals/ (x-(2*y)+6)+(3*(sqrt(x)))

Integral of (x-(2y)+6)+(3(sqrt(x))) dx

The solution

You have entered [src]

  4                           
  /                           
 |                            
 |  /                  ___\   
 |  \x - 2*y + 6 + 3*\/ x / dx
 |                            
/                             
0

$$\int\limits_{0}^{4} \left(3 \sqrt{x} + \left(\left(x - 2 y\right) + 6\right)\right)\, dx$$

Integral(x - 2*y + 6 + 3*sqrt(x), (x, 0, 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. Integrate term-by-term:
  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:
      
      $\int \left(- 2 y\right)\, dx = - 2 x y$
    The result is: $\frac{x^{2}}{2} - 2 x y$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 6\, dx = 6 x$
  The result is: $\frac{x^{2}}{2} - 2 x y + 6 x$
The result is: $2 x^{\frac{3}{2}} + \frac{x^{2}}{2} - 2 x y + 6 x$
Add the constant of integration:

$2 x^{\frac{3}{2}} + \frac{x^{2}}{2} - 2 x y + 6 x+ \mathrm{constant}$

The answer is:

$2 x^{\frac{3}{2}} + \frac{x^{2}}{2} - 2 x y + 6 x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                          
 |                                   2                       
 | /                  ___\          x       3/2              
 | \x - 2*y + 6 + 3*\/ x / dx = C + -- + 2*x    + 6*x - 2*x*y
 |                                  2                        
/

$$\int \left(3 \sqrt{x} + \left(\left(x - 2 y\right) + 6\right)\right)\, dx = C + 2 x^{\frac{3}{2}} + \frac{x^{2}}{2} - 2 x y + 6 x$$

Simplify

The answer [src]

48 - 8*y

$$48 - 8 y$$

48 - 8*y

$$48 - 8 y$$

48 - 8*y

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x-(2y)+6)+(3(sqrt(x))) dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x-(2*y)+6)+(3*(sqrt(x))) dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of (x-(2y)+6)+(3(sqrt(x))) dx