- #1

Yankel

- 395

- 0

I am trying to solve the integral:

\[\int cot(x)\cdot csc^{2}(x)\cdot dx\]

If I use a substitution of u=cot(x), I get

\[-\frac{1}{2}cot^{2}(x)+C\]

which is the correct answer in the book, however, if I do this:

\[\int \frac{cos(x)}{sin^{3}(x)}dx\]

I get, using a substitution u=sin(x)

\[-\frac{1}{2}csc^{2}(x)+C\]

which according to MAPLE, is also correct. In addition, according to MAPLE the move I made for the new function, is also correct !

I am confused !