Intergral Partial Fraction


With the previous method we cannot (will be difficult) to neutralize the forms as below
∫ 5x (2x – 4) dx or ∫ 2x sin x dx.

To solve the form of the equation, let us consider the following steps.
If f and g are differential functions, the rule applies.


If we integrate the rule, we will get it


To further simplify the form we can write it with

u = f(x)            du = f ’(x) dx
v = g(x)           dv = g ‘(x) dx

so, the formula can be simplified as follows.

∫ u dv = uv - ∫ v du

Example 1.
Solve the integral results of ∫ 12x (2x - 3)3 dx
Answer:
If it is known that,


So that, 

Example 2.
Solve the integral results of ∫ 12x (2x - 3)3 dx
Answer:
If it is known that,


So that,


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