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The key here is to realise that tanx = sinx/cosx. If we write out the left hand side of the equation in terms of sine and cosine we get: cosx/sinx + sinx/cosx These two fractions can be put over a common ...

the aim of finsing the inverse is making x the subject. To start we need to multiply both sides by: (2x+3), giving us:

y(2x+3) = 5x-4

now we need to expand the brackets:

To integrate the product of two functions - say f(x) = xsinx, the product of g(x) = x and h(x) = sin(x) - the we use integration by parts. 

Since integration is the inverse of differentia...

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: