Author Topic: Antidifferentiation help (Read 1148 times) Tweet Share

cns1511 · « **on:** May 20, 2009, 06:17:28 pm »

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.

Damo17 · « **Reply #1 on:** May 20, 2009, 06:27:20 pm »

Quote from: cns1511 on May 20, 2009, 06:17:28 pm

(Image removed from quote.)

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.

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

$=2 log_e(x^2+2)$

GerrySly · « **Reply #2 on:** May 20, 2009, 06:28:50 pm »

Let $u=x^2+2$
Therefore $\frac{du}{dx}=2x$
Equivalent to $dx=\frac{du}{2x}$
$\begin{align*} \int \frac{4x}{x^2+2} dx &= \int \frac{4x}{u} \frac{du}{2x}\\ &= \int \frac{2}{u} du\\ &= 2\log_e{(x^2+2)} \end{align*}$

cns1511 · « **Reply #3 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

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