# Let's do some calculus! (19)

Calculus Level 3

$\begin{eqnarray} I_{1} & = & \displaystyle \int_{0}^{{\pi}/{2}} {\dfrac{\sin x - \cos x}{1 + \sin x \cos x}} \,dx \\ \\ I_{2} & = & \displaystyle \int_{0}^{2 \pi} {{\cos}^{6}x} \,dx \\ \\ I_{3} & = & \displaystyle \int_{{-\pi}/{2}}^{{\pi}/{2}} {{\sin}^{3}x} \,dx \\ \\ I_{4} & = & \displaystyle \int_{0}^{1} {\ln \left( \dfrac{1}{x} - 1 \right)} \,dx \end{eqnarray}$

From the given anti-derivatives above, find the one whose value is not equal to $$0$$. If the anti-derivative is $$I_{n}$$ where $$n \in \{1,2,3,4\}$$, submit your answer as $$n$$.

Notation: $$\ln \left( \cdot \right)$$ denotes the natural logarithm function.