Question

Find the integral:
(x+2)(x-3)^1/2

Answer 1

what mean the exponent 1/2 ?

Answer 2

sqrt

Answer 3

yes right

so than how will be your exercise ?

Answer 4

Dint getcha!!

Answer 5

\[\int(x-2)(x-3)^{\frac{1}{2}}dx\]
Let u = x-3
du = ... ?

Answer 6

1

Answer 7

dx

Answer 8

Hmm...
du = (1) dx
So, du = dx

x-2 = (x-3)+1 = u+1

So, the integral becomes
\[\int (u+1)u^{\frac{1}{2}} du\]
Can you find the integral now?

Answer 9

X-2 is raised to power sqrt(1/2)

Answer 10

Is the question (a)\[\int(x-2)(x-3)^{\frac{1}{2}}dx\]
Or (b)
\[\int[(x-2)(x-3)]^{\frac{1}{2}}dx\]?

Answer 11

Integral of { (x+2)*((x-3)^1/2)}

Answer 12

@cambrige Expand \(\bf u^{1/2}(u+1)\) and then integrate.

Answer 13

how to expand u^1/2???

Answer 14

x+2 = x-3 + 3 +2 = (x-3) + 5 = u+5
So, the integral becomes
\[\int (u+5)u^\frac{1}{2}du\]

Answer 15

@Callisto Where did the u + 5 come from. Isn't it supposed to be u + 1?

Answer 16

The asker typed the question wrong. Check his/her previous comment.

Answer 17

still not gtin

Answer 18

Which part?

Answer 19

doent match with ans

Answer 20

*doesnt

Answer 21

Have you integrated it?

Answer 22

ans_ {2(3x+16)((x-3)^3/2)}/16+c

Answer 23

yes

Answer 24

Would you mind showing your work?

Answer 25

wait a sec

Answer 26

1 min\

Answer 27

I dont even know if its correct!!

Answer 28

Expand \((u+5)*u^\frac{1}{2}\), can you?

Answer 29

tryin now

Answer 30

By distributive property

Answer 31

Calm...
What do you get when you expand (a+2)a?

Answer 32

a^2+2a

Answer 33

Yes.
Same thing here.
You need to expand \((u+5)u^\frac{1}{2}\) first. What do you get when you expand \((u+5)u^\frac{1}{2}\)?

Answer 34

{u^2+5u}/u^1/2

Answer 35

That is \(u^\frac{3}{2} + 5u^\frac{1}{2}\)
Now, can you integrate \(u^\frac{3}{2} + 5u^\frac{1}{2}\) with respect to u, that is can you solve
\[\int u^\frac{3}{2} + 5u^\frac{1}{2}du\]?

Answer 36

I don't know how you got the first step.

Answer 37

No. You don't have to change the variable now. You change the variable after you finish doing \(\int u^\frac{3}{2} + 5u^\frac{1}{2}du\)
What have you got when you do \(\int u^\frac{3}{2} + 5u^\frac{1}{2}du\)?

Answer 38

in terms of u.

Answer 39

why to integrate again??

Answer 40

Check the second term. Something wrong with that.

Answer 41

Also, after you integrate it, remove the integral sign and "du".

Answer 42

ya....sry bout dat!!.....nothing wrong with 2nd term!

Answer 43

Sorry, my mistake about the second term.
So, we get \[\frac{2u^\frac{5}{2}}{5} + \frac{10u^\frac{3}{2}}{3}+C\]
Next, replace all u by x-3. Then we're done.

Answer 44

tryin

Answer 45

matches with the ans