ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: cns1511 on May 20, 2009, 06:17:28 pm

Title: Antidifferentiation help
Post by: cns1511 on May 20, 2009, 06:17:28 pm: (http://i132.photobucket.com/albums/q39/cns1511/Untitled-5.jpg)

I have my derivative $\frac{2x}{x^2+2}\$

But I don't know how I am meant to get 4x instead of 2x.

Thanks.
Title: Re: Antidifferentiation help
Post by: Damo17 on May 20, 2009, 06:27:20 pm: Quote from: cns1511 on May 20, 2009, 06:17:28 pm
(http://i132.photobucket.com/albums/q39/cns1511/Untitled-5.jpg)

I have my derivative $\frac{2x}{x^2+2}\$

But I don't know how I am meant to get 4x instead of 2x.

Thanks.

$2\int \frac{2x}{x^2+2} dx$ $= \int \frac{4x}{x^2+2} dx$

$=2 log_e(x^2+2)$
Title: Re: Antidifferentiation help
Post by: GerrySly on May 20, 2009, 06:28:50 pm: Let $u=x^2+2$
Therefore $\frac{du}{dx}=2x$
Equivalent to $dx=\frac{du}{2x}$
$\begin{align*} \int \frac{4x}{x^2+2} dx &= \int \frac{4x}{u} \frac{du}{2x}\\ &= \int \frac{2}{u} du\\ &= 2\log_e{(x^2+2)} \end{align*}$
Title: Re: Antidifferentiation help
Post by: cns1511 on May 20, 2009, 10:25:25 pm: Quote from: GerrySly on May 20, 2009, 06:28:50 pm
Let $u=x^2+2$
Therefore $\frac{du}{dx}=2x$
Equivalent to $dx=\frac{du}{2x}$
$\begin{align*} \int \frac{4x}{x^2+2} dx &= \int \frac{4x}{u} \frac{du}{2x}\\ &= \int \frac{2}{u} du\\ &= 2\log_e{(x^2+2)} \end{align*}$
Thanks :)