Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*exp(-4*x)
Integral of 1/(x^2-2*x)
Integral of x(1+x)^1/2
Integral of tg^5x/cos^2x
Identical expressions
one /(3x-5x)
1 divide by (3x minus 5x)
one divide by (3x minus 5x)
1/3x-5x
1 divide by (3x-5x)
1/(3x-5x)dx
Similar expressions
1/(3*x-5*(x)^(1/2))
1/(3x+5x)

Integral of 1/(3x-5x) dx

The solution

You have entered [src]

 oo             
  /             
 |              
 |      1       
 |  --------- dx
 |  3*x - 5*x   
 |              
/               
2

$$\int\limits_{2}^{\infty} \frac{1}{- 5 x + 3 x}\, dx$$

Integral(1/(3*x - 5*x), (x, 2, oo))

Detail solution

Let $u = - 5 x + 3 x$ .

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

$\int \left(- \frac{1}{2 u}\right)\, du$
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:

$- \frac{\log{\left(- 5 x + 3 x \right)}}{2}$
Now simplify:

$- \frac{\log{\left(- 2 x \right)}}{2}$
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(3*x - 5*x)
 | --------- dx = C - --------------
 | 3*x - 5*x                2       
 |                                  
/

$$\int \frac{1}{- 5 x + 3 x}\, dx = C - \frac{\log{\left(- 5 x + 3 x \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$$-\infty$$

-oo

$$-\infty$$

-oo

Use the examples entering the upper and lower limits of integration.

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 1/(3x-5x) dx

Limits of integration:

The graph:

Piecewise:

The solution