Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sin²xcos²x
Integral of x*2^(-x)
Integral of (1/x^2)dx
Integral of x²ln(x)
How do you in partial fractions?:
(x^2)/(1+x)
Graphing y =:
(x^2)/(1+x)
Identical expressions
(x^ two)/(one +x)
(x squared ) divide by (1 plus x)
(x to the power of two) divide by (one plus x)
(x2)/(1+x)
x2/1+x
(x²)/(1+x)
(x to the power of 2)/(1+x)
x^2/1+x
(x^2) divide by (1+x)
(x^2)/(1+x)dx
Similar expressions
(x^2)/(1-x)

Solving integrals/ (x^2)/(1+x)

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

The solution

You have entered [src]

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

$$\int\limits_{0}^{1} \frac{x^{2}}{x + 1}\, dx$$

Integral(x^2/(1 + x), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{x^{2}}{x + 1} = x - 1 + \frac{1}{x + 1}$
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:
  
  $\int \left(-1\right)\, dx = - x$
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:
  
  $\log{\left(x + 1 \right)}$
The result is: $\frac{x^{2}}{2} - x + \log{\left(x + 1 \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/2 + log(2)

$$- \frac{1}{2} + \log{\left(2 \right)}$$

-1/2 + log(2)

$$- \frac{1}{2} + \log{\left(2 \right)}$$

-1/2 + log(2)

Numerical answer [src]

0.193147180559945

0.193147180559945

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 (x^2)/(1+x) dx

Limits of integration:

The graph:

Piecewise:

The solution