Find S (long integral sign) (x^1/2 - 4) (x^-1/2 - 1)dx.

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Question

Find S (long integral sign) (x^1/2 - 4) (x^-1/2 - 1)dx.

Show Workout Step by Step Please
Thank you

hartnn · Answer

can you foil ? 
(a+b)(c+d) = ... ?

tkhunny · Answer

Entirely algebraic.  What's stopping you from multiplying the two factors and having only exponents you can deal with?

anonymous · Answer

I can't do the x^1/2 times by the x^-1/2.....what would I get?

hartnn · Answer

yeah, after you multiply u get three terms,
and you use the fact that integral x^n dx = x^{n+1}/(n+1) +c

hartnn · Answer

the 
$\huge {x}^{1/2}\times x^{-1/2}=x^{1/2+(-1/2)}=...? $

anonymous · Answer

Yeah lol

tkhunny · Answer

For $a\ne0$, we have $a\cdot\dfrac{1}{a} = a^{1}\cdot a^{-1} = a^{1-1} = a^{0} = 1$

anonymous · Answer

Would that give me x^0 which would make x^1 or just 1?

hartnn · Answer

x^0 =1 yes

anonymous · Answer

I got it thanks

hartnn · Answer

cool :)
welcome ^_^

hartnn · Answer

and WELCOME to OpenStudy :D

tkhunny · Answer

You DO have to stay away from x = 0.

anonymous · Answer

Thanks... Got it @tkhunny and thanks @hartnn. I'll be on here a lot more now haha :D

hartnn · Answer

Glad to hear that :)