# Homework Help: Immediate integral problem

1. Jan 18, 2009

### Dell

4$$\int$$9$$\frac{1-\sqrt{x}}{\sqrt{x}+2}$$

what i did:
t=$$\sqrt{x}$$
x=t2
dx=x'dt=2tdt

now my integration is from 2-3 instead of 4-9

$$\int$$$$\frac{1-t}{t+2}$$2tdt=2$$\int$$$$\frac{t-t2}{t+2}$$dt

=2($$\int$$$$\frac{t}{t+2}$$dt-$$\int$$$$\frac{t2}{t+2}$$dt)

the 1st integral i can replace with$$\int$$1-$$\frac{2}{t+2}$$dt which is an immediate integral, but how do i simplify the second part??

2. Jan 18, 2009

### Dick

Re: Integration

Just divide t+2 into t^2 using polynomial division. Actually, you might want to take a step by and divide t-t^2 by t+2.

3. Jan 18, 2009

### Dell

Re: Integration

i get t+3-[6/(t+2)]

so i get --->2[(t^2)/2]+3t-6ln|t+2|]
is this right??

4. Jan 18, 2009

### Dick

Re: Integration

Sure.

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