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Integral of d{x}:
Integral of x^(1/3)
Integral of sin(x)^4
Integral of cos(x)^3
Integral of (e^(x^2))
Identical expressions
(-x)/((two *y))
( minus x) divide by ((2 multiply by y))
( minus x) divide by ((two multiply by y))
(-x)/((2y))
-x/2y
(-x) divide by ((2*y))
(-x)/((2*y))dx
Similar expressions
(x)/((2*y))

Solving integrals/ (-x)/((2*y))

Integral of (-x)/((2*y)) dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} \frac{\left(-1\right) x}{2 y}\, dx$$

Integral((-x)/((2*y)), (x, 0, 1))

Detail solution

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

$\int \frac{\left(-1\right) x}{2 y}\, dx = \frac{1}{2 y} \int \left(- x\right)\, dx$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x\right)\, dx = - \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- \frac{x^{2}}{2}$
So, the result is: $- \frac{x^{2} \frac{1}{2 y}}{2}$
Now simplify:

$- \frac{x^{2}}{4 y}$
Add the constant of integration:

$- \frac{x^{2}}{4 y}+ \mathrm{constant}$

The answer is:

$- \frac{x^{2}}{4 y}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /              2  1 
 |              x *---
 | -x              2*y
 | --- dx = C - ------
 | 2*y            2   
 |                    
/

$$\int \frac{\left(-1\right) x}{2 y}\, dx = C - \frac{x^{2} \frac{1}{2 y}}{2}$$

Simplify

The answer [src]

-1 
---
4*y

$$- \frac{1}{4 y}$$

=

-1 
---
4*y

$$- \frac{1}{4 y}$$

-1/(4*y)

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