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Integral of d{x}:
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Identical expressions
(-2x)/(x+ one)
( minus 2x) divide by (x plus 1)
( minus 2x) divide by (x plus one)
-2x/x+1
(-2x) divide by (x+1)
(-2x)/(x+1)dx
Similar expressions
(-2x)/(x-1)
(1-2*x)/((x+1)^2+4)^(0,5)
(2x)/(x+1)

Integral of (-2x)/(x+1) dx

The solution

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  1         
  /         
 |          
 |   -2*x   
 |  ----- dx
 |  x + 1   
 |          
/           
0

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

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

Detail solution

Rewrite the integrand:

$\frac{\left(-1\right) 2 x}{x + 1} = -2 + \frac{2}{x + 1}$
Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-2\right)\, dx = - 2 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{2}{x + 1}\, dx = 2 \int \frac{1}{x + 1}\, dx$
  1. Let $u = x + 1$ .
    
    Then let $du = dx$ and substitute $du$ :
    
    $\int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    Now substitute $u$ back in:
    
    $\log{\left(x + 1 \right)}$
  So, the result is: $2 \log{\left(x + 1 \right)}$
The result is: $- 2 x + 2 \log{\left(x + 1 \right)}$
Add the constant of integration:

$- 2 x + 2 \log{\left(x + 1 \right)}+ \mathrm{constant}$

The answer is:

$- 2 x + 2 \log{\left(x + 1 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                                  
 |  -2*x                            
 | ----- dx = C - 2*x + 2*log(1 + x)
 | x + 1                            
 |                                  
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2 + 2*log(2)

$$-2 + 2 \log{\left(2 \right)}$$

-2 + 2*log(2)

$$-2 + 2 \log{\left(2 \right)}$$

-2 + 2*log(2)

Numerical answer [src]

-0.613705638880109

-0.613705638880109

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

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Identical expressions

Similar expressions

Integral of (-2x)/(x+1) dx

Limits of integration:

The graph:

Piecewise:

The solution