- (1) \( \displaystyle \int x(x + 5)^3 \, dx \)
- (2) \( \displaystyle \int \dfrac{e^{2x}}{e^{2x} + 2} \, dx \)
- (3) \( \displaystyle \int \dfrac{dx}{x(5\log x + 3)^2} \)
- (4) \( \displaystyle \int_{-2}^{3} (x - 3)(x + 2) \, dx \)
- (5) \( \displaystyle \int_{\frac{\pi}{3}}^{\frac{\pi}{2}} \sin^3 x\cos^2 x \, dx \)
※\( \cos \frac{\pi}{2} = 0 \), \( \cos \frac{\pi}{3} = \frac{1}{2} \)