Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of (1+x)/x
Integral of 1/5x
Integral of xsin(x)cos(x)
Integral of 4x³dx
How do you in partial fractions?:
x^2/(x+4)
Graphing y =:
x^2/(x+4)
Identical expressions
x^ two /(x+ four)
x squared divide by (x plus 4)
x to the power of two divide by (x plus four)
x2/(x+4)
x2/x+4
x²/(x+4)
x to the power of 2/(x+4)
x^2/x+4
x^2 divide by (x+4)
x^2/(x+4)dx
Similar expressions
x^2/(x-4)

Solving integrals/ x^2/(x+4)

Integral of x^2/(x+4) dx

The solution

You have entered [src]

  1         
  /         
 |          
 |     2    
 |    x     
 |  ----- dx
 |  x + 4   
 |          
/           
0

$$\int\limits_{0}^{1} \frac{x^{2}}{x + 4}\, dx$$

Integral(x^2/(x + 4), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{x^{2}}{x + 4} = x - 4 + \frac{16}{x + 4}$
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:
  
  $\int \left(-4\right)\, dx = - 4 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{16}{x + 4}\, dx = 16 \int \frac{1}{x + 4}\, dx$
  1. Let $u = x + 4$ .
    
    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:
    
    $\log{\left(x + 4 \right)}$
  So, the result is: $16 \log{\left(x + 4 \right)}$
The result is: $\frac{x^{2}}{2} - 4 x + 16 \log{\left(x + 4 \right)}$
Add the constant of integration:

$\frac{x^{2}}{2} - 4 x + 16 \log{\left(x + 4 \right)}+ \mathrm{constant}$

The answer is:

$\frac{x^{2}}{2} - 4 x + 16 \log{\left(x + 4 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                        
 |    2            2                      
 |   x            x                       
 | ----- dx = C + -- - 4*x + 16*log(4 + x)
 | x + 4          2                       
 |                                        
/

$$\int \frac{x^{2}}{x + 4}\, dx = C + \frac{x^{2}}{2} - 4 x + 16 \log{\left(x + 4 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-7/2 - 16*log(4) + 16*log(5)

$$- 16 \log{\left(4 \right)} - \frac{7}{2} + 16 \log{\left(5 \right)}$$

-7/2 - 16*log(4) + 16*log(5)

$$- 16 \log{\left(4 \right)} - \frac{7}{2} + 16 \log{\left(5 \right)}$$

-7/2 - 16*log(4) + 16*log(5)

Numerical answer [src]

0.0702968210273561

0.0702968210273561

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/(x+4) dx

Limits of integration:

The graph:

Piecewise:

The solution