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The question says to use integration by parts on this question, but at the minute we only have one variable.

Therefore, we introduce a 1, so that log|x|= 1*log|x|, here we have not altere...

We can start by letting y = ln(x)

What we are trying to show is that dy/dx = 1/x

Since y = ln(x), then e^y = e^ln(x) = x

Taking the derivat...

When differentiating, you want to use the formula ax^n differentiates to (an)x^(n-1), so for the example above, x^3 where a is 1, and n is 3, the differentiation is (13)x^(3-1) which results t...

This is a question taken from a core 4 paper and is a typical example of a differential equation question.

The first thing to notice about this equation is that it is "separable"...

Find dy/dx where y = (x²+7)^1/2
=> 1/2(x²+7)^-1/2 * d/dx(x²+7)  By the chain rule
=> 1/2(x²+7)^-1/2 * 2x
=>...