Consider the following statements: (c or C is the constant of integration)
Statement 1.
Let $S\left(x\right)=\int \frac{dx}{e^x+8e^{-x}+4e^{-3x}},R\left(x\right)=\int \frac{dx}{e^{3x}+8e^x+4e^{-x}},$  .
 If  $M\left(x\right)=\frac{1}{2}{\tan }^{-1}\left(f\left(x\right)\right)+c$  where c is an arbitrary constant then  $f\left({\log }_e^2\right)=\frac{3}{2}$.
Statement 2.  
 $\int \frac{e^{\cot x}}{{\sin }^{2}x}(2\ln \cos ecx+\sin 2x)dx=-2e^{\cot x}\ln \left(\cos ecx\right)+c$   where c is an arbitrary constant.
Statement 3.  
If  $\int \frac{{\sec }^{2}x-2010}{{\sin }^{2010}x}dx=\frac{P\left(x\right)}{{\sin }^{2010}x}+C,$  then value of  $\left[P\left(\frac{\pi }{3}\right)\right]=0$  (Where [.] denotes G.I.F).
 Statement 4. 
 If   $\int \frac{dx}{{\sin }^{6}x+{\cos }^{6}x}={\cot }^{-1}\left(f\left(x\right)\right)+c$ then  $\left[f\left(\frac{\pi }{6}\right)\right]=$0 (Where [.] denotes G.I.F).
 Correct statement(s) is (are)