Bài 5 trang 113 SGK Giải tích 12. Tính các tích phân sau

Trung bình: 4,56
Đánh giá: 48
Bạn đánh giá: Chưa

a) 011+3x32dx ; b) 012x3-1x2-1dx ; c) 12ln1+xx2dx.

 


a) 011+3x32dx=13011+3x32d1+3x=1321+3x52501=21525-1=6215.

b) 012x3-1x2-1dx=012x-1x2+x+1x-1x+1dx=012x2+x+1x+1dx=012x2+xx+1+1x+1dx=012xx+1x+1+1x+1dx=012x+1x+1dx=x22+lnx+1012=18+ln32.

c) 12ln1+xx2dx

+) Đặt u=ln1+xdv=1x2dxta có du=ln1+x'dx=11+xdxv=1x2dx=-1x.

+) Khi đó 12ln1+xx2dx=-1xln1+x12-12-1xdxx+1=-12ln3-ln2+121xx+1dx=ln2-12ln3+121x-1x+1dx=ln2-12ln3+lnx-ln1+x12=ln2-12ln3+ln2-ln3-ln1-ln2=3ln2-32ln3=ln2333=3ln233.