- #1

Potatochip911

- 318

- 3

## Homework Statement

As I've been going through examples in my textbook they are becoming increasingly lengthy to compute and thus I have resorted to using software to complete the task. For example when computing the series for ##\sin{(\ln{(1+x)})}## $$\ln{(1+x)}=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+... \\ \sin{x}=x-\frac{x^3}{3!}+\frac{x^5}{5!}+... \\

\sin{(\ln{(1+x)})}=\sin{(x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4})}\\

=(x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4})-\frac{(x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4})^3}{3!}+\frac{(x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4})^5}{5!}

$$

## Homework Equations

3. The Attempt at a Solution [/B]

This would take a ridiculously long time to calculate by hand (for me at least) and I was just curious as to whether or not it's normal to encounter difficult expressions to evaluate by hand when finding Maclaurin series.