ページ3:

部分積分法の基本練習 ①
log x dx
log x = (log x)·1 = (log x) (x)' #5
[logx dx = [(log x) (x)'dx
微分形に
= (log x) x = √(log x)'. x dx
.
-
そのまま・積分 微分・積分
=
x log x-x dx
=
x logx - fdx
= xlog x-x+С > R

ページ4:

2x
部分積分法の基本練習 ③
√x e²x dx
x-e' = (x) (1/2e^*)' 指数の方を微分形に
√x e³dx = f(x)·(½ e²y dx
=
=
=
=
=
1
|21-2 1-2 1-2
2x
ter
xe
―
-
xe
2x
-
-xe
2x
-
1
2x dx
2x dx
Je²
22
1
4
2x
e²x² + C
+ C
dx

ページ5:

部分積分法の基本練習 ④
√ (log x)² dx
(log x)' = (log x)2(x)'対数ぢゃない方を
√ (log x)² dx
= √(log x)². (x)'dx
=
微分形に
- √(2 log x · ±)-(x) dx
= (log x)² · (x) = √(2 log x
•
= x(log x)² - 2√log x dx
=
=
2
X
x(log x)² - 2(x log x − x + C)
2
-
x(log x)² - 2x log x+2x+C