Integration Problem (1 Viewer)

someth1ng · May 17, 2012

Integrate: (2x)/[(x^2+2x+5)^2] from -1 to 1 but don't worry about the limits. I just can't do the integrating.

SpiralFlex · May 17, 2012

$\int \frac{2x}{((x+1)^2+4)^2} \;dx$

$$Let x+1=2\tan \theta$

$x=2\tan \theta-1$

$dx=2\sec^2 \theta\; d \theta$

$= \int \frac{2*(2\tan \theta-1)}{(4\sec^2 \theta)^2} 2\sec^2 \theta \; d\theta$

$= \int \frac{2*(2\tan \theta-1)}{(8\sec^2 \theta)} \; d \theta$

$=\int \frac{4\tan \theta - 2}{8\sec^2 \theta} \; d \theta$

$=\int (\frac{1}{2}\cos \theta \sin \theta-\frac{1}{4}\cos^2 \theta) \; d \theta$

$Continue.$

someth1ng · May 17, 2012

Oh, I didn't know you could use the tan and sec sub in these questions...

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Integration Problem (1 Viewer)

someth1ng

Retired Nov '14

SpiralFlex

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someth1ng

Retired Nov '14

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