a) \[ \int x \cdot e^x \, dx = e^x (x - 1) + C \]
b) \[ \int \ln(x) \, dx = x (\ln(x) - 1) + C \]
c) \[ \int x \cdot \cos(x) \, dx = x \cdot \sin(x) + \cos(x) + C \]
d) \[ \int x \cdot \ln(x) \, dx = \frac{x^2}{2} \cdot \ln(x) - \frac{x^2}{4} + C \]
e) \[ \int x \cdot \sin(x) \, dx = -x \cdot \cos(x) + \sin(x) + C \]
f) \[ \int x^2 \cdot e^x \, dx = e^x (x^2 - 2x + 2) + C \]
