Question

integrate this one please......

Answer 1

\[\int\limits_{}^{} \frac{\sqrt{x}+5}{\sqrt{x}-2} dx\]

Answer 2

I think you should prefer Rationalization here..

Answer 3

yes, please, i have my answer but i checked it by differentiation, and i got a wrong answer, i want know where is my mistake

Answer 4

You should show your work so that we can find where you have done wrong..

Answer 5

ok,

Answer 6

Need not to be fast..
Take your time..

Answer 7

oh, it's alright now, i saw where i've done wrong. thanks though. :)

Answer 8

Sure??

Answer 9

help me again please. @waterineyes

Answer 10

Where??

Answer 11

can you show me how you solve it? i'm confused

Answer 12

I said you to use rationalization here..

Multiply and divide by \(\sqrt{x} + 2\)..

Answer 13

just take \[\sqrt{x}=t\]

Answer 14

write, \[\sqrt{x}+5=\sqrt{x}-2 +3\]

Answer 15

that means x=t^2 and dx=2tdt

Answer 16

then the integration becomes,
\[(1+3/t-2 )2tdt\]

Answer 17

i think you can go ahead from here?

Answer 18

ok, thanks. :)

Answer 19

rationalize it will get easy .

Answer 20

@sami-21 i think rationalising makes it a lil difficult.never mind. thats my opinion

Answer 21

after having \[2\int\limits_{}^{} \frac{u^2 +5u}{u-2} du\]
what shal i do?
i tried using long division, and after that,

Answer 22

@vamgadu @waterineyes

Answer 23

stick with the long division, that's the way to go.

Answer 24

How did you get it??

Answer 25

you should get something like that.

\[ u+7+\frac{14}{u-2}\]

Answer 26

i got \[2\int\limits_{}^{} (u+7+\frac{14}{u-2}) du\]

Answer 27

Separate them..

Answer 28

then i got \[u^2 +14u+28 \ln |u-2|+ C\]

Answer 29

Absolutely...

Answer 30

What else you want??
This is the answer dude..

Answer 31

not quiet, back substitution

Answer 32

if i substitute \[\sqrt{x} =u\]

Answer 33

Of if you made any substitution then replace u by that..

Answer 34

i got \[x +14\sqrt{x} +28 \ln |\sqrt{x} -2| +C\]

Answer 35

Right..
Well done..

Answer 36

but if i get the dervative of it, i should have obtained the problem, but i don't.

Answer 37

oh, i got it already. when i get the derivative of x i thought it was 0, it should be 1, thanks to you all!! :)