Evaluate $\int_{-1}^{1} 5 x^{4} \sqrt{x^{5}+1} d x$.

$\int_1^e \frac{1 + \log x}{x} \, dx = $

Let $\alpha$ and $\beta$ $(\alpha < \beta)$ be the roots of $18x^2 - 9\pi x + \pi^2 = 0$,$f(x) = x^2$,and $g(x) = \cos x$. Then $\int_{\alpha}^{\beta} x (g \circ f(x)) dx =$

$\int_0^1 \frac{1}{2+\sqrt{x}} \, dx =$

$\int_{8}^{18} \frac{1}{(x+2) \sqrt{x-3}} \, dx = $

Evaluate the integral $\int_{0}^{\frac{\pi}{2}} \frac{\sin x}{1+\cos ^{2} x} \,d x$.