# APM - Q3 - Trig. integrals

> Source: https://ollybritton.com/notes/maths/problems/advanced-problems-in-mathematics/q3/ · Updated: 2022-03-04 · Tags: advanced-problems-in-mathematics, notes, maths

## Flashcards
### 2022-03-04
##### What is $$\int \frac{\cos x - \sin x}{\cos x + \sin x}$$??
$$
\ln(\cos x + \sin x) + c
$$

Because of the chain rule.

##### If you have $$I_1 = \int\frac{\cos x}{a\cos x + b \sin x} \text{d}x$$ $$I_2 = \int\frac{\sin x}{a\cos x + b\sin x}$$ then what could you do to make a nice integral by combining them that you could evaluate??
$$
aI_1 + bI_2 = \int \frac{a\cos x + b\sin x}{a\cos x + b \sin x} \text{d}x
$$

$$
bI_1 - aI_2 = \int \frac{b \cos x - a \sin x}{a \cos x + b \sin x} \text{d}x
$$

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