Twenty minutes or less.

5-minute version

Open the cheatsheet. Look at the four core rules:

$$\int x^{n}dx=\frac{x^{n+1}}{n+1}+c(n\ne -1)\int \frac{1}{x}dx=\ln |x|+c$$ $$\int e^{x}dx=e^x+c\int \sin xdx=-\cos x+c\int \cos xdx=\sin x+c$$

That’s 80% of every workshop question. The other 20% is the $\frac{1}{a}$ you tack on for $(ax+b)$ forms.

20-minute prep plan

Time	Action
0–5 min	Skim the cheatsheet rule tables and do 3 easy quiz questions.
5–10 min	Do one worked example from each PDF: an indefinite, a definite, then a “find the constant.”
10–15 min	Take the cheatsheet quiz to completion.
15–20 min	Read the in-depth note section on the chain-rule reversal — the $\frac{1}{a}$ explained.

What to revise first

If you only have time for one thing: the $\frac{1}{a}$ rule. It is the single most common mark-loser.

$$\int e^{2x}dx=\frac{1}{2}{e}^{2x}+c\int \cos (3x)dx=\frac{1}{3}\sin (3x)+c$$ $$\int \frac{1}{2x+1}dx=\frac{1}{2}\ln |2x+1|+c\int (5x+1{)}^{4}dx=\frac{(5x+1{)}^5}{5\cdot 5}+c$$

Key formulas

$$\int x^{n}dx=\frac{x^{n+1}}{n+1}+c(n\ne -1)$$ $$\int \frac{1}{x}dx=\ln |x|+c\int e^{x}dx=e^x+c$$ $$\int e^{ax+b}dx=\frac{1}{a}{e}^{ax+b}+c\int \frac{1}{ax+b}dx=\frac{1}{a}\ln |ax+b|+c$$ $$\int \cos xdx=\sin x+c\int \sin xdx=-\cos x+c\int {\sec }^{2}xdx=\tan x+c$$ $${\int }_a^{b}f(x)dx=F(b)-F(a)\text{(top minus bottom)}$$

Likely workshop tasks

Task type	What to do
Indefinite integrals	Apply power, exponential, trigonometric, and $\frac{1}{x}$ rules
Recover $f(x)$ from $f^{\prime }(x)$	Integrate $f^{\prime }(x)$ and add $+c$
Definite integrals	Find $F(x)$, then compute $F(b)-F(a)$
Find an unknown constant	Evaluate the definite integral, set it equal to the target, solve
Area under a curve	Sketch first, split at roots if needed, then handle sign

Mistakes to avoid

• Forgetting $+c$ on indefinite integrals.
• Forgetting the $\frac{1}{a}$ on chain-rule reversals.
• Using the power rule on $1/x$.
• Confusing definite integral with geometric area on a curve that dips below the x-axis.
• Swapping the order of subtraction. It is $F(b)-F(a)$.

Mini self-test

Five minutes. No notes.

1. $\int \left(4x^3-\frac{6}{x}+2\sin x\right)dx=?$
2. ${\int }_0^{2}3x^{2}dx=?$
3. Given ${\int }_{-1}^k(-12x+9)dx=15$, find non-zero $k$.

Answers:

Question	Answer
1	$x^4-6\ln |x|-2\cos x+c$
2	$8$
3	$k=\frac{3}{2}$

Done checklist

• Cheatsheet glanced at.
• Three worked examples in pen.
• Cheatsheet quiz attempted.
• Mini self-test attempted.

That’s enough. Stop here.

Source files used

• school-stuff/EGD105-Calculus/Week11/Integration Rules.pdf
• school-stuff/EGD105-Calculus/Week11/Integration Exercises.pdf
• school-stuff/EGD105-Calculus/Week11/Definite Integration Exercises.pdf