The Mathematical Ninja pointed out of the window. “I CAN SEE MY CAR MAKING SMOKE!”, he yelled.

The student looked out of the window, said “Oh no!” and then, after a pause. “Hang on, you don’t have a car.”

The Mathematical Ninja smiled. “Correct. But you’ll now remember how to integrate trig functions:

• I - when you’re integrating
• can - starts with C, meaning $\cos$, which integrates to…
• see - starts with S, meaning $\sin$, which integrates to…
• my car - starts with MC, meaning $-\cos$, which integrates to…
• making smoke - starts with MS, meaning $-\sin$.

“And $-\sin$ integrates back to $\cos$?” asked the student.

“Correct. Also, when you’re integrating, you tend to divide - which means $\int \sin(2x) dx$ would be…?”

“Uh… $-\frac{1}{2} \cos(2x)$?” said the student. “Plus a constant!” he added, hurriedly, catching the Mathematical Ninja’s raised eyebrow.