# How the Mathematical Ninja integrates

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.