Integration with possible U-substitution?

Question

anonymous · Answer

$$\int\limits_{1}^{2}\frac{ 7x+1 }{\sqrt(x )}$$

anonymous · Answer

Steps on how to do it would be awesome.

terenzreignz · Answer

I'm going to see about the integral without the limits first...
$$\Large \int \frac{7x+1}{\sqrt{x}}dx$$(not forgetting of course that this is still possible without using any substitutions at all...)

terenzreignz · Answer

Proceeding at your signal @kobesaurus

anonymous · Answer

ok im all ears.

anonymous · Answer

@terenzreignz

terenzreignz · Answer

U-subsitution?  It simply has to be U-substitution? :)

anonymous · Answer

no not at all, that was just my assumption!

terenzreignz · Answer

Okay... maybe if we write it this way...
$$\Large \int \frac{7x+1}{x^{\frac12}}dx$$does that help?

anonymous · Answer

I tried doing (7x+1)(x^-1/2) and then distributing but would that be ok?

terenzreignz · Answer

Yes.  And you should get...
$$\Large \int\left(7x^{\frac12}+x^{-\frac12}\right)dx$$
However cumbersome, you may now use the power rule for integration... ;)

anonymous · Answer

oooo, I see what I did. 7x * x^-1/2 =/= x^3/2 lol. wow i noobed it up good.

terenzreignz · Answer

So, got it from here?

anonymous · Answer

absolutely! Thanks boss

terenzreignz · Answer

*Terence*
and no problem :)