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education/math/MATH1220 (calc II)/Integration with Trig Identities.md
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@ -54,4 +54,14 @@ $$ \theta = \arctan(\frac{x}{2}) $$
7. Rewriting the equation with $\theta$ in terms of x, we get: 7. Rewriting the equation with $\theta$ in terms of x, we get:
$$ \frac{3}{2}\arctan(\frac{x}{2}) + C$$ $$ \frac{3}{2}\arctan(\frac{x}{2}) + C$$
This means that: This means that:
$$ \int\frac{3}{4+x^2}dx = \frac{3}{2}\arctan(\frac{x}{2}) + C $$ $$ \int\frac{3}{4+x^2}dx = \frac{3}{2}\arctan(\frac{x}{2}) + C $$
# A VERY LARGE LIST OF TRIG IDENTITIES FOR CALCULUS
| non calc identities<br> |
| ------------------------------------ |
| $\csc(x) = \dfrac{1}{sin(x)}$ |
| $\sec(x) = \dfrac{1}{\cos(x)}$ |
| $\cot(x) = \dfrac{1}{\tan(x)}$ |
| $\tan(x) = \dfrac{\sin(x)}{\cos(x)}$ |
| $\sin^2(x) + \cos^2(x) = 1$ |