⑩天掌 Teaching Plan on Advanced Mathematics 例2计算 sin'x-sinxdx 3 解:∫(x)=√sin3x-sin°x=cosx(sinx) T sin'x-sin xdx=l cos x(sin x 2dx 2 cos x(sinx2dx cosrIsinr )2d 2 sinx)id sinx-[(sin sin SIn x SIn 0 5
Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 例2 计算 sin sin . 0 3 5 x − xdx 解 f x x x 3 5 ( ) = sin − sin ( )2 3 = cos x sin x − 0 3 5 sin x sin xdx ( ) = 0 2 3 cos x sin x dx ( ) = 2 0 2 3 cos x sin x dx ( ) − 2 2 3 cos x sin x dx ( ) = 2 0 2 3 sin x d sin x ( ) − 2 2 3 sin x d sin x ( ) 2 0 2 5 sin 5 2 = x ( ) − 2 2 5 sin 5 2 x . 5 4 =
⑩天掌 Teaching Plan on Advanced Mathematics d x 例3计算 ex√lnx(1-lnx) 解原式 d(Inx) nx nx d(ln x) d √Inx n nx 2 nx T 2arcsin(Inx
Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 例3 计算 . ln (1 ln ) 4 3 − e e x x x dx 解 原式 − = 4 3 ln (1 ln ) e (ln ) e x x d x − = 4 3 ln (1 ln ) e (ln ) e x x d x − = 4 3 2 1 ( ln ) ln 2 e e x d x 4 3 2 arcsin( ln ) e e = x . 6 =