Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^(33/10)/5
Integral of 1/(2*x)
Integral of 1/(sqrt(1+x^2))
Integral of 1/tanx
Graphing y =:
1/(2*x)
Sum of series:
1/(2*x)
Limit of the function:
1/(2*x)
Identical expressions
one /(two *x)
1 divide by (2 multiply by x)
one divide by (two multiply by x)
1/(2x)
1/2x
1 divide by (2*x)
1/(2*x)dx
Similar expressions
1/(2x-1)²
1/(2x^2+3x+1)
(x^2+2x-1)/(2x^3+3x^2-3x)
1/(2*x^2+6*x-2)
(2x-1)/(2x^2+8x-6)

Solving integrals/ 1/(2*x)

Integral of 1/(2*x) dx

The solution

You have entered [src]

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

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

Detail solution

Let $u = 2 x$ .

Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :

$\int \frac{1}{2 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{2}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{2}$
Now substitute $u$ back in:

$\frac{\log{\left(2 x \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

22.0452230669964

22.0452230669964

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 1/(2*x) dx

Limits of integration:

The graph:

Piecewise:

The solution