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Often, it can seem daunting when you are asked to differentiate a function that looks particularly messy. However, it's really quite simple if you break it down in easy to manage steps....

How to integrate ln(x)?

In order to integrate log x of base e, we are going to apply integration by parts.

Recall that the formula for integration by parts i...

We all know the the square root of 2 is irrational. So, the answer should be no. But how do we prove it?Let's assume for contradiction that x²=2 and that x is rational. Then x can be expressed ...

Let's take a positive integer n.We can write it as a product of prime numbers:n=p₁p₂...p_r, where p₁, p₂, ..., p_r are prime factors of n.No...

Normal manipulation of inequalities does not affect the direction of the inequality such as:
addition
subtraction
multiplication or division by a positive number,