Question

evaluate the integral by using multiple substitutions

Answer 1

\[∫\frac{ \sin \sqrt{t} }{ \sqrt{tcos ^{3}\sqrt{t}} }dt\]

Answer 2

this is equal to:

\[=\int\limits_{}^{}\frac{ \sin(\sqrt{t}) }{ \sqrt{t}\cos^{3/2}(\sqrt{t}) }\]

let u = cos(sqrt(t))
du = \[\frac{ - \sin{\sqrt{t}} dt }{ 2 \sqrt{t} }\]

Answer 3

what is the next step?

Answer 4

\[= -(1/2) \int\limits_{}^{} \frac{ du }{ u^{3/2} }\]

Answer 5

\[-\frac{ 2 }{ t \frac{ 3 }{ 2 } }+c\]

Answer 6

none of the answers seem to be the one you gave. except this one looks kinda close

Answer 7

integral of that is u^(-1/2) = \[\frac{ 1 }{ \sqrt{\cos{\sqrt{t}}} }\]

Answer 8

multiplied by 4

Answer 9

\[\frac{ 4 }{ \sqrt{\cos \sqrt{t}} }+c\]

Answer 10

divided by 2 twice when i should have multiplied. sorry. not using paper >.<

Answer 11

is another possible answer but im notsure

Answer 12

you got it

Answer 13

its the answer i have

Answer 14

100% sure

Answer 15

the last one i just gave?

Answer 16

\[-\frac{ 4 }{ \sqrt{\cos \sqrt{t}} }+c\]

Answer 17

positive 4

Answer 18

ok so this without the negative?

Answer 19

yes

Answer 20

are you sure?

Answer 21

100%

Answer 22

did it on paper

Answer 23

ok thanks