x=e^u

dx=e^udu

Original formula = ∫ sinu e udu

= ∫ Xinu de^u

Xinu e u-∫ e udsinu

E u-∫ e u university

Xinu e u-∫ cosude u

New e^u -e^u University+∫ E UDCOSU Campus

= New e^u -e^u University-New e^udu University

The two sides merged, so

* New e Udu =1/2× e U Island (New Coase Island)+C.

therefore

Original formula =1/2 x (sinlnx-coslnx)+C.

8( 1) Original formula =∫(x- 1+2)/(x- 1)? Advanced (short for deluxe)

=∫ 1/(x- 1)？ +2∫ 1/(x- 1)？ Advanced (short for deluxe)

=- 1/(x- 1)+2× 1/(-3+ 1)(x- 1)^(-3+ 1)+c

=- 1/(x- 1)-(x- 1)^(-2)+c

=- 1/(x- 1)- 1/(x- 1)？ +c