- Demonstrate how to evaluate each of the following integrals. \[ \int\frac{1}{x^2+1}\,\mathrm{d}x \quad \int\frac{x}{x^2+1}\,\mathrm{d}x \quad \int\frac{x^2}{x^2+1}\,\mathrm{d}x \quad \int\frac{x^3}{x^2+1}\,\mathrm{d}x \] \[ \int\frac{\tan(x)}{\cos(x)}\,\mathrm{d}x \quad \int \tan(x) \,\mathrm{d}x \quad \int \tan(x)\cos(x) \,\mathrm{d}x \quad \int \tan(x)\cos^2(x)\,\mathrm{d}x \] \[ \int\frac{\ln(x)}{x}\,\mathrm{d}x \qquad \int\ln(x)\,\mathrm{d}x \qquad \int x\ln(x) \,\mathrm{d}x \]