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The problem with this equation lies with the denominator on the left hand side. If we recall our graph of ln(x) however, we know that ln(x) is always positive and not equal to 0. Now we can safely multipl...

Z is simply a general complex number, which can be written as Z = x+iyHere |Z-2+3i| = 1 can be written as |Z-(2-3i)| = 1, which is just an expression for every Z whose distance from the point (2,-3i) is e...

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...