Solve the following integrals. Use 'C' as the integrating constant in your answers.\\
a) $\int x^2 \cos(x^3 + 2) \, dx = \frac{1}{3} \sin(x^3 + 2) + C$\\
b) $\int \frac{x}{\sqrt{1 - 4x^2}} \, dx = -\frac{1}{4} (1 - 4x^2)^{\frac{1}{2}} + C$\\
c) $\int_0^3 (x - 1)^6 \, dx = 4971027$\\
d) $\int 2x(x^2 + 2)^5 \, dx = \frac{1}{6} (x^2 + 2)^6 + C$\\
e) $\int xe^{x^2} \, dx = \frac{1}{2} e^{x^2} + C$\\
f) $\int_0^1 \frac{e^x + 1}{e^x} \, dx = \frac{e^2}{2} + e - \frac{3}{2}$\\
g) $\int \frac{x}{x^2 + 5} \, dx = \frac{1}{2} \ln(|x^2 + 5|) + C$\\
h) $\int -\sin(t) \cos^4(t) \, dt = \frac{1}{5} \cos^5(t) + C$\\
i) $\int (2x - 3)^{19} \, dx = \frac{1}{40} (2x - 3)^{20} + C$
