問題：次の式を計算せよ
- (1) \( \displaystyle \int 3\sin^3 x\cos x dx \)
- (2) \( \displaystyle \int \dfrac{3x}{\sqrt{x^2 + 9}} dx \)
- (3) \( \displaystyle \int \dfrac{5}{3x(\log x + 1)^2} dx \)
- (4) \( \displaystyle \int \dfrac{1}{\sqrt{x^2 + 16}} dx \)
- (5) \( \displaystyle \int \dfrac{2e^{4x}}{e^{2x} + 1} dx \)
- (6) \( \displaystyle \int_{-3}^{2} (x - 2)^2(x + 3) dx \)
- (7) \( \displaystyle \int_{1}^{\sqrt{3}} \dfrac{1}{x^2\sqrt{4 - x^2}} dx \)