三角関数の積分法(integration of trigonometric functions)

演習問題

1.: 次の積分を求めよう．
(a): $\displaystyle{\int{\sin^3{x}} dx}$
(b): $\displaystyle{\int{\sin^2{3x}} dx}$
(c): $\displaystyle{\int{\sin^3{x}\cos^2{x}} dx}$
(d): $\displaystyle{\int{\cos{3x}\sin{2x}} dx }$
(e): $\displaystyle{\int{\sin^5{x}} dx}$
(f): $\displaystyle{\int{\sec^2{\pi x}} dx}$
(g): $\displaystyle{\int{\tan^3{x}} dx}$
(h): $\displaystyle{\int{\tan^2{x}\sec^2{x}} dx}$
(i): $\displaystyle{\int{\tan^3{x}\sec^3{x}} dx}$
(j): $\displaystyle{\int{\sec^5{x}} dx}$
(k): $\displaystyle{\int{\frac{dx}{3 - 2\cos{x}}}}$
(l): $\displaystyle{\int{\frac{\sin{x}}{2 - \sin{x}}} dx}$
(m): $\displaystyle{\int{\frac{1 + \sin{x}}{1 + \cos{x}}} dx}$
(n): $\displaystyle{\int{\frac{\sin^2{x}}{\sin^2{x} - \cos^2{x}}} dx}$
(o): $\displaystyle{\int{\frac{dx}{1 + \tan{x}}}}$