Question

integration of 1/2x-3 dx​

Answer 1

Given: Equation 1/(2x-3)

To find: Integration of 1/2x-3 dx​

Solution:

• So to find the integration of the above equation,

• Consider A = ∫ 1/(2x - 3)    dx

• Now here, we can say that x is an independent variable.

• So, to find the integral in A, lets use substitution method,

• Put

                    2x - 3 = y

• Now taking differentiation on both side we get,       2 dx - 0 = dy

  dx = dy/2

• Now substituting the value of dx and (2x-3) in in A, we get:

• A = ∫dy/2y = (1/2) ∫dy/y = (1/2) . log y + C

• Now converting to the original equation in terms of x,

• Putting value of y in A, we get:

• A = (1/2) . log (2x - 3) + C ................(where C = constant )

Answer:

                 Integration of 1/2x-3 dx​ is  (1/2) . log (2x - 3) + C

Answer 2

Step-by-step explanation:

x

∫1/(2−3x)2dx=−∫−1/(2−3x)2dx=−(1/2−3x/−3)=1/3(2−3x)+c