高等数学A上册习题解答 至微分中值定理(16)

华中师范大学专用

(12)

1

sinxcos4dx

=

xsin2x+cos2xdx

=

sinxcos4xsinx

1 +dxsinx

sin2x+cos2=dx+xdx

= dcosx sinx1

cosx+[cosx+sinx

]dx

=

1

3cos3x+1cosx+ln|tanx2

|+C.(12)

1

sindx

==u=cos====x

==

xcosx 1(1 u2)udu

=

4

1

11 u2 1 u2 u4dx=11 u112ln1+u+u+3u

=112ln

1 cosx1+cosx+3cos3x+1cosx

+C.16

(0.41)

(0.42)