Evaluate the integral using a trig substitution: `int x^3/(sqrt(4+x^2)) dx`
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Inna Shpiro
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In this case, this would be x = 2tan(t).
This is because the the trigonometric identity `tan^2(t) + 1 = sec^2(t)` can then be applied:
`sqrt(4 + x^2) = sqrt(4 + 4tan^2(t)) = sqrt(4(tan^2(t) + 1)) `
`= sqrt(4sec^2(t)) = 2sec(t)`
Also, if x = 2tan(t), then `dx = 2sec^2(t)dt` and `x^3 = 8tan^3(t)dt`
Plugging all this into original integral, we get
`int (8tan^3(t))/(2sec(t)) 2sec^2(t)dt`
This simplifies to
`int...
(The entire section contains 235 words.)
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