Maths Integration Problem HELP

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Maths Integration Problem! HELP!

Homework Statement


ok maths problems is like this:
2.g. integrate (2x-1)/*square root x*

The Attempt at a Solution



ok. i split the equation up so that i am integrating 2x/*root x* - 1/*root x*

the 1/root x integrates to - 2x^(1/2) and the constant is present (+c)

but i cannot seem to integrate the (2x)/(x^(1/2))
the answer is (4/3)x^(3/2)... but i can't seem to get it... even working backwards.
 
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Can you simplify \frac{x}{\sqrt{x}} ?
 
take the two out the front of the integral sign and then multiply?
 
ok. i don't get where the x^(3/2) comes from.
\frac{x}{\sqrt{x}}
becomes x.x^(-1/2)... then we add the powers?
= x^(1/2)?
 
Yes, correct. Can you integrate now?
 
Yes, correct. Can you integrate now?
 
x^(1/2) becomes (2/3)x^3/2) then multiplying in the two becomes...

(4/3)x^(3/2) which is correct yeh?

cool :D



ok another one. (1-4x)/(x*root*x)... i can't do the (4x)/(x^(3/2))
 
4 \cdot \frac{x}{x^{1.5}}= 4 \cdot x^{-1/2}
 
damn it. lol. how stupid of me. missed the cancelling there totally. ah! no wonder i could do the rest of the chapter *shakes head*
 
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