Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of (dy)/(2y-3)
Integral of 2/x³
Integral of 1/(4-3cos(x))
Integral of √x⁴-2x³+x²
Identical expressions
(dy)/(2y- three)
(dy) divide by (2y minus 3)
(dy) divide by (2y minus three)
dy/2y-3
(dy) divide by (2y-3)
Similar expressions
(dy)/(2y+3)

Solving integrals/ (dy)/(2y-3)

Integral of (dy)/(2y-3) dx

The solution

You have entered [src]

  1             
  /             
 |              
 |       1      
 |  1*------- dy
 |    2*y - 3   
 |              
/               
0

$$\int\limits_{0}^{1} 1 \cdot \frac{1}{2 y - 3}\, dy$$

Simplify

Detail solution

Let $u = 2 y - 3$ .

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

$\int \frac{1}{4 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{2 u}\, du = \frac{\int \frac{1}{u}\, du}{2}$
  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:

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

$\frac{\log{\left(2 y - 3 \right)}}{2}$
Add the constant of integration:

$\frac{\log{\left(2 y - 3 \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(2 y - 3 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 |      1             log(2*y - 3)
 | 1*------- dy = C + ------------
 |   2*y - 3               2      
 |                                
/

$${{\log \left(2\,y-3\right)}\over{2}}$$

Simplify

The answer [src]

-log(3) 
--------
   2

$$-{{\log 3}\over{2}}$$

-log(3) 
--------
   2

$$- \frac{\log{\left(3 \right)}}{2}$$

Simplify

Numerical answer [src]

-0.549306144334055

-0.549306144334055

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 (dy)/(2y-3) dx

Limits of integration:

The graph:

Piecewise:

The solution