Question

Integrate :

Answer 1

\[\int\limits_{}^{} \frac{ x }{ \sqrt{4+x ^{2}} }dx=\]

Answer 2

put x^2+4=u

Answer 3

Ok so i substitute it, What next ??

Answer 4

\[x=\sqrt{u-4}\]

Answer 5

dx= ?

Answer 6

ohh i should derivate it

Answer 7

lol. no , don't try to find x....

Answer 8

differentiate this :
x^2+4=u

Answer 9

dx=du/2x

Answer 10

that is
xdx = du/2
ok?

Answer 11

Yeah right

Answer 12

so u get int of 1/ root u du/2
right ?

Answer 13

\[\int\limits_{}^{}\frac{ du }{ \sqrt{u} 2}\]

Answer 14

yup, so 1/root u = u^{what} ?

Answer 15

u^-1/2

Answer 16

can u integrate that?

Answer 17

2u^1/2

Answer 18

isn't it just root u ?

Answer 19

yeah If we cancel it Only root u is left what next ??

Answer 20

resubstitute u = ....

Answer 21

add +c in the end

Answer 22

\[\sqrt{4+x ^{2}}+c\]

Answer 23

that is correct.

Answer 24

Thankyou very Much :)

Answer 25

welcome ^_^