$$ \int e^x\left[\frac{x^2+1}{(x+1)^2}\right] d x \quad \text { is equal to } $$

$$ \int \frac{f^{\prime}(x)}{f(x) \log (f(x))} d x \text { is equal to } $$

$$ \int \log x(\log x+2) d x \text { equals to } $$

$$ \int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x \text { is equal to } $$