Question

Integrate the following:

Answer 1

\[∫ \sqrt{\frac{ 2 }{ 5x }} dx\]

Answer 2

\[\int\limits_{}^{}\frac{ (2/5)^\frac{ 1 }{ 2 } }{ x^\frac{ 1 }{ 2 }}\]

Answer 3

@bmelyk did you figure out the other one?

Answer 4

is that the first step?

Answer 5

well you can go about this many ways, but personally that's how i start

Answer 6

okay so then what

Answer 7

well the 2/5 is a constant, so you really only need to worry about x

Answer 8

ok

Answer 9

\[(\frac{ 2 }{ 5 })^\frac{ 1 }{ 2 }\int\limits_{}^{}(\frac{ 1 }{ x })^\frac{ 1 }{ 2}\]

Answer 10

thats what i have so far.

Answer 11

(1/x)^(1/2) is also just x^(-1/2)

Answer 12

okie

Answer 13

so then just integrate x^(-1/2)

Answer 14

how do i go about that? lol, we just started this course last week

Answer 15

ill just use my formula, right?

Answer 16

um i dont know what you mean by formula, but anytime you integrate you are raising x by a power. So like x would become (x^2)/2.

Answer 17

i got: \[\sqrt{\frac{ 2 }{ 5 }} \frac{ -2 }{ 3 } x ^{\frac{ -3 }{ 2 }} +c\]

Answer 18

Close, but you took the derivative of x (kinda)
x^(-1/2) would become 2x^(1/2)
-1/2+1=1/2

Answer 19

so its\[\sqrt{\frac{ 2 }{ 5 }} 2\sqrt{x}+c?\]

Answer 20

yes i believe so

Answer 21

can you help me with antoher'?

Answer 22

sure

Answer 23

okay... \[∫ (\sec^23x+\frac{ 1 }{ 3x }) dx\]

Answer 24

alright, well \[\sec ^2x \] is a known derivative of tanx

Answer 25

yes

Answer 26

1/x is the derivative of natural log

Answer 27

yes