Question

antiderivative of cotx

Answer 1

Anti-derivative is a term used in Calculus to mean Integral.

So, in simple terms, $\textbf{we are asked to find the integral of cot x}$

So we have to find the expression of:

$\displaystyle \int cot \, x \, dx$

We start by taking:

$cot \, x = \frac{\cos x}{\sin x}$

Then we notice that cos x is the derivative of sin x. So we substitute $\sin x = u$


And then we have the simple integration formula:

$\displaystyle \int \frac{dx}{x} = ln \, \mid x \mid$

Finally we have the solution:

$\boxed{\displaystyle \int cot \, x \, dx = ln \, \mid \sin x \mid + c}$


The solution is also shown in the image.