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)**.
What is the Integration of UV Formula (Integration by Parts)?
Integration by parts: ∫u·v dx = u∫v dx − ∫(u'·∫v dx)dx. ILATE rule for choosing u. Solved examples with full working.
How to Integrate x²? (Formula & Solution)
Learn the exact mathematical solution to integrate x^2 dx. Understand the Power Rule of Integration and why we must always add the constant 'C' at the end.
What is the Meaning of Intersecting Lines in Geometry?
Learn the exact mathematical meaning of Intersecting Lines in geometry. Understand the 'Point of Intersection', vertical angles, and how they differ from parallel lines.
Is 0 a Rational Number?
Yes, 0 is a rational number because it can be written as 0/1 (p/q form where q ≠ 0). 0 is also an integer, whole number, and natural number boundary. Explained with proof.
Is Pi (π) a Rational or Irrational Number?
Is Pi a rational number? Discover why the mathematical constant Pi (π) is strictly an Irrational Number, despite the common fraction 22/7 used in school.
Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.