Evaluate the indefinite integral using the method of substitution: $\int \frac{x^2}{1 + x^6} \, dx$.

Evaluate the integral using integration by parts: $\int x \sin(2x) \, dx$.

Find the area of the region bounded by the parabola $y = 4 - x^2$ and the x-axis ($y = 0$).

Evaluate the following standard indefinite integrals: (a) $\int \left(3x^4 - 5x^2 + \frac{2}{x} - e^{3x} + 4\right) dx$ (b) $\int \frac{x^2}{x^2 + 1} dx$ (c) $\int \tan^2 x \, dx$