We use the integration by parts scheme to address integrals with powers of x multiplied by ln(x)

The scheme already discussed for writing down the reults from integration by parts is applied to cyclic integration by parts where the integrand contains a product of an exponential and a sin or cosine.

We write the directional derivative on a surface z=z(x,y) in terms of the grad operator acting on z as a dot product with a unit vector in the direction required.

We investigate the rule for differentiating an inverse function then make some observations about reciprocals of 1st and 2nd derivatives.

We prepare integral from 0 to 2 Pi of 1/(2+cos(theta)) for integration in the complex plane.

We prove the formulae for sin(A+B) and cos(A+B) using Euler's results for sine and cos. The other sum and difference formulae work in a similar way.

We complete the integration introduced in part 1, using Cauchy's residue theorem.

We attempt to evaluate an integral that is not well-defined and investigate how this problem manifests itself in the complex contour version of the integral.

We demonstrate how periodicity of a function affects the Laplace transform.

We evaluate another integral similar to that in parts 1 and 2 but containing a sine rather than a cosine. Here we prepare the integral for contour integration.