部分積分法(integration by parts)

演習問題

1.: 次の不定積分を求めよう．
(a): $\displaystyle{\int{x\log{x}} dx}$
(b): $\displaystyle{\int{x^2e^{-x}} dx}$
(c): $\displaystyle{\int{(\log{x})^2} dx}$
(d): $\displaystyle{\int{x(x+5)^{14}} dx}$
(e): $\displaystyle{\int{x\cos{x}} dx}$
(f): $\displaystyle{\int{e^{x}\sin{x}} dx}$
(g): $\displaystyle{\int{\log{(1+x^2)}} dx}$
(h): $\displaystyle{\int{x\tan^{-1}{x}} dx}$
(i): $\displaystyle{\int{x^n\log{x}} dx}$ (nは整数)
(j): $\displaystyle{\int{x^3\sin{x}} dx}$
(k): $\displaystyle{\int{x\sinh{x}} dx}$