$$\int {{{(\ln x)}^{ - 1}}dx - \int {{{(\ln x)}^{ - 2}}dx} } $$ is equal to ?

What is $$\int {{{dx} \over {x({x^7} + 1)}}} $$ equal to ?

What is $$\int {{{({x^{e - 1}} + {e^{x - 1}})dx} \over {{x^e} + {e^x}}}} $$ equal to ?

Let f(x) be an indefinite integral of sin²x.

Consider the following statements

Statement I The function f(x) satisfies f(x + $$\pi$$) = f(x) for real x.

Statement II sin²(x + $$\pi$$) = sin²x for all real x.

Which one of the following is correct in respect of the above statements?