客幸制三L则由不定积分药铁元公式计算出 ∫4=∫-m=∫ cos4 r =-r+x-a=-r+3rn-3+ra =+22-++ 1 (cos)-3-3(c0)c0cos+c. 5.求∫2dx 解设tanr=t,则d=dr ∫女=∫女=jam+e =e+1+内i=2+=号+t+e=号mrz+mz+e 6.求∫cos sin3xdr cos rsin rdr=-cos r sin?rdcos-cos (1-cos )dcos 数学分析山试题第4页（共8页） 4. ➛ R sin7 x cos4 x dx ❽ ❡✲ cos x = t, ❑❞Ø➼➮➞✛❺✄ú➟❖➂Ñ Z sin7 x cos4 x dx = Z − sin6 x cos4 x d cos x = Z −(1 − t 2 ) 3 t 4 dt = − Z 1 − 3t 2 + 3t 4 − t 6 t 4 dt = − Z t −4 dt + 3 Z t −2 dt − 3 Z dt + Z t 2 dt = − 1 1 − 4 t 1−4 + 3 1 1 − 2 t 1−2 − 3t + 1 3 t 3 + c = 1 3 (cos x) −3 − 3(cos x) −1 − 3 cos x + 1 3 cos3 x + c. 5. ➛ R sin2 x+1 cos4 x dx ✮ ✗tan x = t, ❑dt = 1 cos2 x dx Z sin2 x + 1 cos4 x dx = Z sin2 x + 1 cos2 x 1 cos2 x dx = Z [tan2 x + sec2 x] 1 cos2 x dx = Z (t 2 + 1 + t 2 )dt = Z 2t 2 dt + Z dt = 2 3 t 3 + t + c = 2 3 tan3 x + tan x + c. 6. ➛ R cos6 x sin3 xdx ✮ Z cos6 x sin3 xdx = Z − cos6 x sin2 xd cos x = Z − cos6 x(1 − cos2 x)d cos x = Z cos8 xd cos x − Z cos6 xd cos x = 1 9 cos9 x − 1 7 cos7 x + c. ê➷➞Û(II)➪❑ ✶ 4 ➄↔✁ 8 ➄↕