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First starting from the right hand side.

 A /(2x + 1) + B /(x + 3) = A(x+3)+B(2x+1)/(x+3)(2x+1)

Therefore the numerator = (A+2B)x+(3A+B)

Equating this numorato...

Firslty, the common rule when differentiating is nx^m has the derivative of (n)(m)x^m-1.

Therefore applying this rule to each individual component of the function:

This equation has one function of x divided by another function of x, we therefore have to use the quotient rule and is written in the form f(x)/g(x). 

The quotient rule is therefore

We use parts for this integration even though there is only one term! make ln(x)=1ln(x)

How to do integration by parts

If you have a function that you need to integra...

Here, we must apply both chain and product rules. The chain rule can be used to find the derivative of a function in the form e^f(x), like this one. However it is useful to know that this will r...