Question

what will be the
integration of 1/(1+x²)½ along x?

Answer 1

\[\int\limits 1/(1+x ^{2})^{1/2}\]
it will be \[\ln (1 + x ^{2})^{1/2}\]

Answer 2

you know that when the numerator is the derivative of the dominator then the integration is ln "dominator"

:)

Answer 3

but the derivative of denominator should be there in the numerator

Answer 4

\[x= \tan \theta\]

Answer 5

ok , the derivative of (x^2 )^1/2 is 1/2 (2x)
so 2 cancel the other 2 :)

Answer 6

and for natural log, exponent should be 1

Answer 7

\[\int\limits 1/x= \ln x\]

Answer 8

if the exponent is other than 1, we use power rule

Answer 9

yeah but we can't multiply it with 2x so ln(1+x²)½ is not the right answer

Answer 10

\[d x= \sec^2 \theta d \theta\]

Answer 11

i think its correct ..
anyways good luck ..

Answer 12

\[\int\limits \sec^2 \theta/(\sqrt{1+\tan^2 \theta} )\]

Answer 13

\[\int\limits \sec^2\theta/\sec \theta d \theta\]

Answer 14

\[\int\limits \sec \theta d \theta\]

Answer 15

\[\ln (\sec \theta + \tan \theta) +C\]

Answer 16

by backward substitution
\[\tan \theta =x\]

Answer 17

yeah that will give us integration of secθ that is ln(secθ+tanθ) and by substituting and we will get probably get ln(sec(tan^-x)+x)

Answer 18

\[\sec \theta =\sqrt{1+x^2}\]

Answer 19

thanks for the help i have some questions on multiple integral usage in finding area and volume. Anyone please help me

Answer 20

post it as a new Q,some one would surly look at it :)

Answer 21

Uzma are you from Pakistan?

Answer 22

ahaa ! ok waiting ur new Qs :)

Answer 23

yes :)

Answer 24

Can you please tell me your qualification and city

Answer 25

what would u do with that :)

Answer 26

nothing just to guess the level of your understanding mathematics

Answer 27

mathematics is as vast, that one can hardly grasp even one area