Question

If I wanted to take the integral of 4/x^2-3, would it be 4ln(x^2-3) divided by the derivative of x^2-3 ?

Answer 1

try differentiating your assumed answer and see whether you get the expression that needs to be integrated

Answer 2

no this is an arctan

Answer 3

So a trig substitution

Answer 4

-4root(3)/3arctan(root3/3)+c

Answer 5

x inside the arctan

Answer 6

Wouldnt deriv of arctan be \[1/(x^2+1)\]

Answer 7

\[-\frac{ 4\sqrt{3} }{ 3 }\arctan(\frac{ \sqrt{2} }{ 3 }x)\]

Answer 8

yes

Answer 9

i proved that using implicit differentiation, or you may use pyth and trig triangle

Answer 10

let me give you the link ...

Answer 11

http://openstudy.com/study#/updates/5111d647e4b09cf125bde79f

Answer 12

http://openstudy.com/study#/updates/5111d647e4b09cf125bde79f

Answer 13

i proved the derivative so you can see the integral ...

Answer 14

integral of the above can be done by substituting x=sqrt(3)*sec u

Answer 15

alternately u can factorise the denominator and apply partial fraction

Answer 16

no its arctanh

Answer 17

its a parabola trig

Answer 18

I got it. I would have to use Partial fractions

Answer 19

yes

Answer 20

but you can use the identity of tanh and just substitute

Answer 21

the required integral is 2/sqrt(3) ln ((x-sqrt(3))/(x+sqrt(3)))+c

Answer 22

i say its a tanh

Answer 23

\[\int\limits \frac{ 4 }{ x^2-3}dx\]

Answer 24

this gives arctanh