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Using integration by parts: split xcos(x) into x multiplied by cos(x). Differentiating x gives 1 and integrating cos(x) gives sin(x). The integral of xcos(x) can therefore be rewritten as xsin(x) - integral ...

Integration by parts formula: ∫ u dv/dx = uv - ∫ du/dx v dx To solve this problem we need to use a trick by thinking of lnx as lnx 1 So we can choose: u=lnx, dv/dx=1 The next step is to find du/dx and v. du/...

So you are asked to find the inverse of a function f(x). The inverse function is denoted by f -1 (x). To help with this we can use the identity f(f -1 (x))=x. Now, we need to define y=f -1 (x). Example: f(x)...

The quotient rule is a formula used to differentiate fractions that contain terms of x in both the numerator and the denominator (we usually refer to this as f(x)/g(x)). As it isn't possible to differentiate...

Sorry in advance for the lack of a diagram, which would have made this explanation so much clearer. Also, the published version of this seems to ignore Unicode formatting, so I will add underscores (_) where...