Finding composite functions of a linear function and an exponential function.

Finding composite functions of a linear function and a logarithmic function.

Finding composite functions of a linear function and a function of the form $x^n+a$.

Finding composite functions of 2 linear functions.

Given a randomised log function select the possible ways of writing the domain of the function.

Find the eigenfunctions of an irregular Sturm–Liouville problem and hence solve an inhomogeneous boundary value problem by writing the solution as an eigenfunction expansion.

Calculating the integral of a function of the form $a \sin(bx)$ using a table of integrals.

Calculating the integral of a function of the form $a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3}$ using a table of integrals. 

Calculating the integral of a function of the form $a \sec^2(bx)$ using a table of integrals.

Calculating the integral of a function of the form $ax^b$ using a table of integrals. 

Calculating the integral of a function of the form $a \cos(bx)$ using a table of integrals.

Integrating an exponential function of the form $ae^{bx}$ using a table of integrals / anti-derivatives.

Calculating the integral of a function of the form $\frac{a}{bx}$ using a table of integrals.

Calculating the integral of a function of the form $\frac{a}{\sqrt{b^2-x^2}}$ using a table of integrals.

Calculating the integral of a function of the form $2ax(ax^2+b)^n$ using integration by substitution. $n$ is a positive or negative fraction.

Calculating the integral of a function of the form $x(ax^2+b)^n$ using integration by substitution.

Calculating the integral of a function of the form $\frac{k(2ax+b)}{ax^2+bx+c}$ using integration by substitution.

Calculating the integral of a function of the form $kx e^{ax^2}$ using integration by substitution, where $k=2na$.

Calculating the integral of a function of the form $\frac{cx+d}{(x+a)(x+b)}$ using partial fractions.

Calculating the integral of a function of the form $ax \cos(x^2+b)$ using integration by substitution.

Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution. $n$ is a positive or negative fraction.

Calculating the integral of a function of the form $\cos(x) \sin^2(x)$ using integration by substitution.

Calculating the integral of a function of the form $\frac{\cos(x) \sin(x)}{(\sin(x)+a)^2}$ using integration by substitution.

Calculating the integral of a function of the form $\frac{\cos(x)}{\sin(x)+a}$ using integration by substitution.

Calculating the integral of a function of the form $\frac{c}{(x+a)(x+b)}$ using partial fractions.

Calculating the integral of a function of the form $e^x \sin(e^x)$ using integration by substitution.

Calculating the integral of a function of the form $2ax(ax^2+b)^n$ using integration by substitution.

Calculating the integral of a function of the form $n x e^{ax^2}$ using integration by substitution.

Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution.

Calculating the integral of a function of the form $kx e^{ax^2}$ using integration by substitution, where $k=2a$.