Question

@Callisto Can you give me some more examples of doing integration "your way"?

Answer 1

\[\int tanx dx\]

Answer 2

\[=\int \frac{sinx}{cosx}dx\]\[=-\int \frac{1}{cosx}d(cosx)\]\[=-\ln|cosx|+C\]
Try:
\[\int cotx dx\]

Answer 3

\[
\begin{align*}
&\int\cot(x)\,dx\\
=&\int\frac{1}{\tan(x)}\,dx\\
=&\int\frac{\cos(x)}{\sin(x)}\,dx\\
=&\int\frac{1}{\sin(x)}\,d(\sin(x))\\
=&\int\ln(\sin(x))
\end{align*}
\]
Seems legit...

Answer 4

No int for the last line
\[=\int\frac{1}{sinx}d(sinx)\]\[=ln|sinx|+C\]