Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of (xcosx)/(2+3x^3)
Integral of 1/(3*x)
Integral of 1/(2x^2-2x+3)
Integral of 1/(1+5x)
Limit of the function:
1/(3*x)
Derivative of:
1/(3*x)
Identical expressions
one /(three *x)
1 divide by (3 multiply by x)
one divide by (three multiply by x)
1/(3x)
1/3x
1 divide by (3*x)
1/(3*x)dx
Similar expressions
((x^3)-1)/(3*(x^4)+x^2+5)
1/(3*x^2-x+1)
Sinx*(cosx)^1/3*x
1/(3x-2)^(1/5)
(1/3x^2-x)

Solving integrals/ 1/(3*x)

Integral of 1/(3*x) dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} \frac{1}{3 x}\, dx$$

Integral(1/(3*x), (x, 0, 1))

Detail solution

Let $u = 3 x$ .

Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :

$\int \frac{1}{3 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{3}$
Now substitute $u$ back in:

$\frac{\log{\left(3 x \right)}}{3}$
Add the constant of integration:

$\frac{\log{\left(3 x \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(3 x \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                     
 |                      
 |  1           log(3*x)
 | --- dx = C + --------
 | 3*x             3    
 |                      
/

$$\int \frac{1}{3 x}\, dx = C + \frac{\log{\left(3 x \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

14.6968153779976

14.6968153779976

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/(3*x) dx

Limits of integration:

The graph:

Piecewise:

The solution