問題：次の問題を解け。
- (1) \( \displaystyle \int_{1}^{2} (3x^2 + 1)\log(x^3 + x) dx \)
- (2) \( \displaystyle \int \biggl( \cos^2\dfrac{x}{2} - \dfrac{1}{2} \biggr)\sqrt{\sin x + 1} dx \)
- (3) \( \displaystyle \int_{-2025}^{2025} \dfrac{12^x + 12^{-x}}{25^x - 25^{-x}} dx \)
- (4) \( 340200\displaystyle \int_{9}^{10} (x - 9)^5(x - 10)^2 dx \)
- (5) \( \displaystyle \int_{-35}^{35} \dfrac{2|x|}{e^x + 1} dx \)