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How to integrate ln(x)?

In order to integrate log x of base e, we are going to apply integration by parts.

Recall that the formula for integration by parts i...

Reminder - a cartesian equation is written in terms of x and y (e.g. y = 2x + 3) while parametric equations are written with x and y separately in terms of t.

Example: Find the cartesian ...

Finding stationary points.

You can find stationary points on a curve by differentiating the equation of the curve and finding the points at which the gradient func...

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) - integr...

Integration by parts formula: ∫ udv/dx = uv - ∫ du/dxv dx

To solve this problem we need to use a trick by thinking of lnx as lnx1
So we can choose: u=lnx, dv/dx=1
...