<math>=\frac{1}{2}\int\frac{2t}{t^2+\frac{3}{4}}\mathrm{d}t+\int\frac{\frac{3}{4}}{t^2+\frac{3}{4}}\mathrm{d}t</math>
<math>=\frac{1}{2}\ln(|t^2+\frac{3}{4})|+\frac{3}{4}\frac{1}{\sqrt{\frac{3}{4}}}\arctan\frac{t}{\sqrt{\frac{3}{4}}}+c</math>
<math>=\frac{1}{2}\ln|(x+\frac{1}{2})^2+\frac{3}{4}|+\sqrt{\frac{3}{4}}\arctan\frac{x+\frac{1}{2}}{\sqrt{\frac{3}{4}}}+c</math>