Maths Integration Problem HELP

[susperia_knvb]

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.

 

[arunbg]

Can you simplify $$\frac{x}{\sqrt{x}}$$ ?

 

[susperia_knvb]

take the two out the front of the integral sign and then multiply?

 

[susperia_knvb]

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)?

 

[arunbg]

Yes, correct. Can you integrate now?

 

[arunbg]

Yes, correct. Can you integrate now?

 

[susperia_knvb]

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))

 

[Gib Z]

$$4 \cdot \frac{x}{x^{1.5}}= 4 \cdot x^{-1/2}$$

 

[susperia_knvb]

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*