3.1 Antiderivatives

1.

(a) $${-\frac{3}{2}x^{-2} + \frac{2}{3}x^{6}}$$(b) $${\frac{t^4}{4} + \tan^{-1}(t)}$$(c) $${-2(\tan{x} - x)}$$(d) $${\frac{2}{7}x^{\frac{7}{2}} + 2x^{\frac{1}{2}}}$$

(e) $${x + \frac{1}{2}\tan^{-1}{\frac{x}{2}}}$$(f) $${\sin^{-1} (\frac{t}{2})}$$(g) $${\frac{x}{2} + \frac{\sin{2x}}{4}}$$(h) $${\log{\vert t + \sqrt{t^2 + 4}\vert}}$$

(i) $${\frac{1}{4}\log{\left\vert\frac{2+x}{2-x}\right\vert}}$$