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Evaluate \[ \int (7x^3 + \frac{1}{2}x^2) dx \]
If \[ \frac{d}{dx} \log x = \frac{1}{x} \quad \quad (\text{A}) \] find \[ \int \frac{1}{x} dx \]
Evaluate \[ \int (x^2 + 1)^2 dx \]
If \[ \frac{d}{dx} \cos x = -\sin x \quad \quad (\text{A}) \] find \[ \int \sin x dx \]