置換積分法(integration by substitution)

演習問題

1.: 次の積分を求めよう．
(a): $\displaystyle{\int{e^{2-x}} dx}$
(b): $\displaystyle{\int{\sec^2{(1-x)}} dx}$
(c): $\displaystyle{\int{\frac{x}{\sqrt{1-x^2}}} dx}$
(d): $\displaystyle{\int{\frac{\sin{x}}{\cos^2{x}}} dx}$
(e): $\displaystyle{\int{\frac{e^{1/x}}{x^2}} dx}$
(f): $\displaystyle{\int{\frac{\sec^2{\theta}}{\sqrt{3\tan{\theta} + 1}}} d\theta}$
(g): $\displaystyle{\int{\frac{1+\cos{2x}}{\sin^2{x}}} dx}$
(h): $\displaystyle{\int{\frac{\log{x}}{x}} dx }$
(i): $\displaystyle{\int{\frac{e^x}{1 + e^{2x}}} dx}$
(j): $\displaystyle{\int{x\sin{(x^2)}} dx}$