$\displaystyle 1.) \quad \int_0^1\frac{x^4+1}{x^6+1}dx$

$\displaystyle 2.) \quad \int_2^3\frac{x}{x^8+1}dx$

$\displaystyle 3.) \quad \int_1^{\sqrt{3}}\frac{x^2+1}{x^4+x^2+1}dx$

$\displaystyle 4.) \quad \int_0^3\arcsin{\sqrt{\frac{x}{x+1}}}dx$

$\displaystyle 5.) \quad \int_{-1}^1\frac{dx}{(e^x+1)(x^2+1)}$

$\displaystyle 6.) \quad \int_{-\pi/4}^{\pi/4}\frac{x^7-3x^5+7x^3-x+1}{\cos^2{x}}dx$

$\displaystyle 7.) \quad \int_0^1\left[\ln\left(x+\sqrt{x^2+1}\right)\right]^2dx$