問題：次の式を計算せよ。
- (1) \( \displaystyle \int_{2}^{4} \dfrac{x^2 + 1}{x^3 - x} dx \)
- (2) \( \displaystyle \int \dfrac{\cos x}{\sin^7 x - \sin x} dx \)
- (3) \( \displaystyle \int_{-1}^{1} \dfrac{2x^2(e^x\sin^2 x + \cos^2 x)}{(x^4 + x^2 + 1)(e^x + 1)} dx \)
- (4) \( \displaystyle \int_{0}^{\frac{\pi}{4}} \sqrt{\tan x} dx \)
- (5) \( \displaystyle \int \dfrac{25}{(2x - 1)\sqrt{-x^2 + x + 6}} dx \)