how to handle fraction + integral?

The equation from my book: (**25.4**)

integral u^n du = u^(n+1) / (n + 1) + c

says in the book its a confusing equation to boot. Can I get an explanation on this quiz question?

Integrate:

x / sqrt(6x^2 + 1)

steps, per answer key:

u = 6x^2 + 1

du = 12x dx

Ok, so u is the denominator, and du is the derivative of the denominator... do I have the wrong equation for this question?? I'll stop there, but the answer key proceeds.

1/12 (int symbol) u ^ -1/2

1/12 2u^1/2

1/6 u^1/2

1/6 (6x^2 + 1)^1/2 + C

Thanks.

Re: how to handle fraction + integral?

Quote:

Originally Posted by

**togo** The equation from my book: (**25.4**)

integral u^n du = u^(n+1) / (n + 1) + c

says in the book its a confusing equation to boot. Can I get an explanation on this quiz question?

Integrate: x / sqrt(6x^2 + 1)

I think that almost always students who are confused by *u-substitution* are so because they fail to consider the derivative.

For example: if $\displaystyle y=\frac{\sqrt{6x^2+2}}{6}$ what is $\displaystyle y'=~?$.

Do all of the steps, carefully and one at a time.