(13)∫x cos(x2)dx;
解 ∫x cos(x2)dx=1∫cos(x2)d(x2)=1sin(x2)+C. 22
(14)∫x
2 3x
x2dx; 解 ∫ 111dx= ∫(2 3x2)2d(2 3x2)= (2 3x2)2+C= 2 3x2+C. 6332 3x211
(15)∫
解 3x31 x43x3dx;
dx= 3134d(1 x)= ln|1 x4|+C. ∫441 x4∫1 x4
(16)∫cos2(ωt+ )sin(ωt+ )dt;
解 ∫cos2(ωt+ )sin(ωt+ )dt=
(17)∫
解 sinxdx; 3cosxsinx1ω2∫cos(ωt+ )dcos(ωt+ )= 1cos3(ωt+ )+C. 3ω11 3 2dx= cosxdcosx=cosx+C=sec2x+C. ∫cos3x∫22
(18)∫
解 sinx+cosx∫sinx cosxdx=∫x cosx( cosx+sinx)
sinx cosxsinx+cosxdx; 1 =∫(sinx cosx)
1 x
9 4x2133d(sinx cosx)=(sinx cosx)3+C. 22 (19)∫dx;
解 ∫1 x
9 4x
1
2∫2dx=∫119 4x2 ∫x9 4x2 =11212x1(x)+∫(9 4x2)=arcsin+9 4x2+C. 89 4x2342223 (x)3