不定積分(indefinite integrals)

演習問題

1.: 次の積分を求めよう．
(a): $\displaystyle{\int (3x^{-3} + 4x^{5}) dx }$
(b): $\displaystyle{\int (t^{3}+ \frac{1}{t^{2}+1}) dt}$
(c): $\displaystyle{\int -2\tan^{2}{x} dx}$
(d): $\displaystyle{\int \frac{x^{3} + 1}{\sqrt{x}} dx}$
(e): $\displaystyle{\int \frac{x^{2} + 5}{x^{2} + 4} dx}$
(f): $\displaystyle{\int \frac{1}{\sqrt{4 - t^{2}}} dt}$
(g): $\displaystyle{\int \cos^{2}{x} dx}$
(h): $\displaystyle{\int \frac{1}{\sqrt{t^{2} + 4}} dt}$
(i): $\displaystyle{\int \frac{1}{4 - x^{2}}dx }$