Find $\displaystyle \int (ax)e^{cx}\; dx $

Find $\displaystyle \int (ax)\ln(cx)\; dx $

Find $\displaystyle \int (ax)\ln(cx)\; dx $

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Split $\displaystyle \frac{b}{(cx + d)(px+q)}$ into partial fractions.

Rearranging equations to change the subject

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx $ 

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.