# how to handle fraction + integral?

• Mar 6th 2013, 08:31 AM
togo
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)

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.
• Mar 6th 2013, 09:12 AM
Plato
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.