Is this integral true? Or is it too much for Wolfram Alpha?

Question

I was playing around with the wolfram calculator, just adding different things and mesmorising at what they equaled, then I randomly put in a bunch of trig functions, and well, this is what I got: $$ \int \cot(x)\cos(x)\sin(x)\tan(x)\sec(x)\csc(x)\,dx = x + C $$

I don't know if this is a standard integral, but I'm pretty sure it's not, I tried googling it but all I found was a mix of random results, can someone please clear this up? I'm sure I can try to integrate this, but I don't want to get a heart-attack.

Answer 1

$$\int \cot x\cos x\sin x\tan x\sec x\csc xdx=\\ \int\frac{\cos x}{\sin x}\cdot\frac{\cos x}{1}\cdot\frac{\sin x}{1}\cdot\frac{\sin x}{\cos x}\cdot\frac{1}{\cos x}\cdot\frac{1}{\sin x}dx=\int 1dx =x+C$$

Answer 2

Try simplifying the integrand by writing $\cot,\tan,\sec,\csc$ all in terms of $\sin,\cos$.

Answer 3

Hint: Suppose I tell you that $\int f(x) dx = x + C$. What can you then deduce about $f(x)$?