Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^(1/2)
Integral of x^1/2
Integral of x*e^(2*x)
Integral of arcsinx
Derivative of:
(x^2+4)/x
Identical expressions
(x^ two + four)/x
(x squared plus 4) divide by x
(x to the power of two plus four) divide by x
(x2+4)/x
x2+4/x
(x²+4)/x
(x to the power of 2+4)/x
x^2+4/x
(x^2+4) divide by x
(x^2+4)/xdx
Similar expressions
(x^2-4)/x

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

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

The solution

You have entered [src]

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

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = x^{2}$ .
  
  Then let $du = 2 x dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{u + 4}{2 u}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{u + 4}{u}\, du = \frac{\int \frac{u + 4}{u}\, du}{2}$
    1. Rewrite the integrand:
      
      $\frac{u + 4}{u} = 1 + \frac{4}{u}$
    2. Integrate term-by-term:
      
      The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
      
      The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{4}{u}\, du = 4 \int \frac{1}{u}\, du$
      
      The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
      
      So, the result is: $4 \log{\left(u \right)}$
      
      The result is: $u + 4 \log{\left(u \right)}$
    So, the result is: $\frac{u}{2} + 2 \log{\left(u \right)}$
  Now substitute $u$ back in:
  
  $\frac{x^{2}}{2} + 2 \log{\left(x^{2} \right)}$
Method #2
1. Rewrite the integrand:
  
  $\frac{x^{2} + 4}{x} = x + \frac{4}{x}$
2. 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 times a function is the constant times the integral of the function:
    
    $\int \frac{4}{x}\, dx = 4 \int \frac{1}{x}\, dx$
    1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
    So, the result is: $4 \log{\left(x \right)}$
  The result is: $\frac{x^{2}}{2} + 4 \log{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                              
 |                               
 |  2               2            
 | x  + 4          x         / 2\
 | ------ dx = C + -- + 2*log\x /
 |   x             2             
 |                               
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

176.861784535972

176.861784535972

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+4)/x dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2