Question

hey guys help me with this

Answer 1

\[\int\limits2x+3/(x-1)(x^2+1) dx = \log{(x-1)^{5/2} (x^2+1)^a} -1/2\tan^{-1} x + A\]

Answer 2

A= constant
a=?
its log to the base e

Answer 3

@Kainui @rational @ParthKohli

Answer 4

@amistre64 integration help

Answer 5

@ikram002p @ParthKohli

Answer 6

@rational @Directrix @divu.mkr

Answer 7

my latex coding fails to load to parsing it might be cumbersome

Answer 8

integrate 2x+3/(x-1)(x^2+1) dx = \log{(x-1)^{5/2} (x^2+1)^a} -1/2\tan^{-1} x + A

yeah, im not sure what im looking at ....

Answer 9

\(\int\limits2x+3/(x-1)(x^2+1) dx =\\ \log{(x-1)^{5/2} (x^2+1)^a} -1/2\tan^{-1} x + A\)

Answer 10

yeah

Answer 11

my idea would be to take the derivative of the right hand side

Answer 12

i dont wanna make guesses, can u really evaluate this integral ?

Answer 13

integral of f'(x) = f(x)+A

d/dx(integral of f'(x)) = d/dx(f(x)+A)

f'(x) = d/dx(f(x)+A)

Answer 14

but is constant or what ?

Answer 15

A------->constant
a------->value to be found

Answer 16

take the derivative of the right side and equate it to the left side

Answer 17

ok :3

Answer 18

im finding this difficult guys :(

Answer 19

you can possibly split the fraction ... decompose it to see how it works into the right side . might be easier might not

Answer 20

\(( \log{(x-1)^{5/2} (x^2+1)^a} -1/2\tan^{-1} x + A)'\)

Answer 21

@ikram002p i should take the derivate of this right

Answer 22

2x+3 A Bx+C
----------- = ----- + ------
(x-1)(x^2+1) x-1 x^2+1


2x+3 = A(x^2+1) + (Bx+C)(x-1)

let x=1

5 = 2A, A = 5/2

let x=0

3 = 5/2 - C, C = -1/2

let x=-1

1 = 5 + 2B +1

B = -5/2

right?

Answer 23

wait let me read

Answer 24

yep

Answer 25

5/2 ln(x-1) - int (5x+1)/(2x^2+2)

thats what i get so far

Answer 26

or the rightest term

-1/2 int [5x/(x^2+1)] -1/2 int[ 1/(x^2+1)]

that gets us to the -1/2 tan^-1 x so its that 5x part we have to work with

Answer 27

-5/2 int [x/(x^2+1)]

-5/4 int [2x/(x^2+1)]

-5/4 log(x^2+1)

Answer 28

so

5/2 log(x-1) -5/4 log(x^2+1) = log{ (x-1)^{5/2} (x^2+1)^a}

log(x-1)^(5/2) + log(x^2+1)^(-5/4) = log{ (x-1)^{5/2} (x^2+1)^a}

log (x-1)^(5/2) (x^2+1)^(-5/4) = log{ (x-1)^{5/2} (x^2+1)^a}

Answer 29

as long as i dint mess it up along the way :) that seems fair to me

Answer 30

hmm

Answer 31

the trick i spose is in decomposing the left side if you are having issues with deriving the right side

Answer 32

wish my latex decoding was working :/

Answer 33

yep
@amistre64
so the value is -5/4
thats right
thank u soooooooooooo much
@amistre64