- #1
Dell
- 590
- 0
4[tex]\int[/tex]9[tex]\frac{1-\sqrt{x}}{\sqrt{x}+2}[/tex]
what i did:
t=[tex]\sqrt{x}[/tex]
x=t2
dx=x'dt=2tdt
now my integration is from 2-3 instead of 4-9
[tex]\int[/tex][tex]\frac{1-t}{t+2}[/tex]2tdt=2[tex]\int[/tex][tex]\frac{t-t2}{t+2}[/tex]dt
=2([tex]\int[/tex][tex]\frac{t}{t+2}[/tex]dt-[tex]\int[/tex][tex]\frac{t2}{t+2}[/tex]dt)
the 1st integral i can replace with[tex]\int[/tex]1-[tex]\frac{2}{t+2}[/tex]dt which is an immediate integral, but how do i simplify the second part??
what i did:
t=[tex]\sqrt{x}[/tex]
x=t2
dx=x'dt=2tdt
now my integration is from 2-3 instead of 4-9
[tex]\int[/tex][tex]\frac{1-t}{t+2}[/tex]2tdt=2[tex]\int[/tex][tex]\frac{t-t2}{t+2}[/tex]dt
=2([tex]\int[/tex][tex]\frac{t}{t+2}[/tex]dt-[tex]\int[/tex][tex]\frac{t2}{t+2}[/tex]dt)
the 1st integral i can replace with[tex]\int[/tex]1-[tex]\frac{2}{t+2}[/tex]dt which is an immediate integral, but how do i simplify the second part??