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(1)/(x(x-1))...

`(1)/(x(x-1))`

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To solve the integral \(\int \frac{1}{x(x-1)} \, dx\), we will use the method of partial fractions. Here’s a step-by-step solution: ### Step 1: Set up the partial fraction decomposition We want to express \(\frac{1}{x(x-1)}\) as a sum of simpler fractions: \[ \frac{1}{x(x-1)} = \frac{A}{x} + \frac{B}{x-1} \] where \(A\) and \(B\) are constants to be determined. ...
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Explore conceptually related problems

Let f(x)=x((1)/(x-1)+(1)/(x)+(1)/(x+1)),x>1

f(x)={(e^((1)/(x-1)))/((1+e^(((1)/(x-1))),x!=1}x-1;x=1)

Knowledge Check

  • Let f(x)= x(1)/(x-1)+(1)/(x)+(1)/(x+1) x lt 1 then

    A
    `f(x) le 1`
    B
    `1 le f(x) le 2`
    C
    `2le f(x) le 3`
    D
    `f(x) gt3`

  • int_(-2)^(3)[cot^(-1)((x-1)/(x+1))+cot^(-1)((x+1)/(x-1))]dx=

    A
    `(5pi)/(2)`
    B
    `(3pi)/(2)`
    C
    `(pi)/(2)`
    D
    `2 cot^(-1)e`

    • Similar Questions

    Explore conceptually related problems

    sin^-1((x-1)/(x+1))+sec^-1((x+1)/(x-1))

    (1)/(x+1)-(1)/(x)<=(1)/(x-1)-(1)/(x-2)

    If x-(1)/(x)=1 , then what is the value of ((1)/(x-1)-(1)/(x+1)+(1)/(x^2 +1)-(1)/(x^2 -1)) ?

    If y=x+(1)/(x+(1)/(x+(1)/(x+(1)/(x+...)))), prove that (dy)/(dx)=(1)/(2(x)/(x+(1)/(x+(1)/(x+1))))

    What is (8x)/(1-x^(4)) - (4x)/(x^(2) +1) +(x+1)/(x-1) - (x-1)/(x+1) equal to?

    Solve: (x+1)/(x-1)-(x-1)/(x+1)=5/6,x!=1,-1

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