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