Question

How to integrate this?

∫(8(x^.5)/(x^2+1)^.5)dx

Answer 1

have you tried direct substitution?

Answer 2

do you mean u-substitution?

Answer 3

yes, the degree of the numerator is one less then that of the denominator, indicating some sort of ln relationship

Answer 4

not sure what to sub...

Answer 5

well, it may have been worth a try...i reach a dead end that way. Are you learning trig substitutions?

Answer 6

x^2+1=u
2x=u'

then...

Answer 7

yeah i was thinking trig substitution, but it has a root x term at the top and i'm not sure how to deal with that using trig sub.

Answer 8

Try:
\[x = \tan \theta\]

This comes from suggested substitutions when you see particular terms under a root sign, leading to pythagorean simplification. first table on first page
http://www.stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-TrigonometSubstitu_Stu.pdf

Answer 9

not sure how to apply it for this case since it has a root at the top and bottom...

Answer 10

This is messed. sure the questions is right? this integral doesn't even want to exist in any tables of integrals i can find

Answer 11

yeah, i'm pretty sure

The original question was to find the volume of the solid when you rotate the area between the two curves:
y= \[\frac{ 4 }{ x^{2}+1 }\] and y=\[\sqrt{x}\]

for the region 0<x<2.3

This question came from expanding the integral

Answer 12

rotate about the x axis i mean

Answer 13

so, the the upper functions change in the middle of that range. You're doing disc?

Answer 14

they intersect at 2.3ish, and i'm using disks

Answer 15

They intersect at appox 1.504
https://www.desmos.com/calculator/qssiomirve

Answer 16

ohhh, i left a square root out, my bad. the denominator of the first function is suppose to have a square root!

Answer 17

\[\frac{ 4 }{ \sqrt{x ^{2}+1} }\]

Answer 18

you may have used the shell equation for your integral, by using the disc, which is pi*r^2, the sqrt signs are destroyed