Bài 4 trang 126+127 SGK Giải tích 12. Tính

Trung bình: 4,63
Đánh giá: 19
Bạn đánh giá: Chưa

a) 2-xsinxdx ; b) x+12xdx ;
c) e3x+1ex+1dx ; d) 1sinx+cosx2dx ;
e) 11+x+xdx ; g) 11+x2-xdx.

 


a) A=2-xsinxdx

+) Đặt u=2-xdv=sinxdxta có du=-dxv=-cosx.

+) Khi đó : A=uv-vdu=-2-xcosx--cosx-dx=x-2cosx-sinx+C.

b) B=x+12xdx=x2+2x+1x12dx=x32+2x12+x-12dx=2x525+22x323+2x121+C=25x5+43x3+2x+C.

c) e3x+1ex+1dx=ex3+1ex+1dx=ex+1e2x-ex+1ex+1dx=e2x-ex+1dx=e2x2-ex+x+C.

d) 1sinx+cosx2dx=12sinx+π42dx=121sin2x+π4dx=-12cotx+π4+C.

e) 11+x+xdx=1+x-x1+x+xdx=1+x2-x21+x+xdx=1+x+x1+x-x1+x+xdx=1+x-xdx=1+x12dx-x12dx=21+x323-2x323+C=231+x3-x3+C.

g) 11+x2-xdx=131+x+132-xdx=1311+x-1x-2dx=13ln1+x-lnx-2+C=13lnx+1x-2+C.