In calculus exams, teachers love to violently throw massive 'trick questions' at students to heavily test their fundamental massive concepts. One of the most famous massive trick questions is asking a student to find the integration of log(2).
Do not heavily confuse ∫ log(2) dx with ∫ log(x) dx. They are completely massively different! The integral of log(x) requires heavy 'Integration by Parts' and the answer is: x*log(x) - x + C.
When a student violently sees the word 'log', they instantly panic and try to apply highly massive, complex integration rules like 'Integration by Parts'.
The fundamental massive rule of calculus states that the integral of any constant 'k' is simply 'k * x'.
Let's evaluate: ∫ log(2) dx
Step 1: Pull the massive constant completely outside the integral sign. = log(2) * ∫ 1 dx
Step 2: The integral of 1 dx is simply 'x'. = log(2) * [ x ]
Step 3: Add the mandatory massive constant of integration 'C'.
Final Answer: = x * log(2) + C
Because log(2) is a massive constant, the derivative of any constant is always absolutely **Zero (0)**.
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