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\int \left | \ln x \right |dx equals ? (0 < x < 1)

  • Option 1)

    x\left ( \left | \ln x \right | \right )-\left ( x-1 \right )+c

  • Option 2)

    x\left ( \left | \ln x \right | \right )-x+c

  • Option 3)

    x\left ( \left | \ln x \right | \right )+\left ( x-1 \right )+c

  • Option 4)

    x+x\left ( \left | \ln x \right | \right )+c

 

Answers (1)

best_answer

As we learnt

Rule for integration by parts -

Take Ist function (u) as according I L A T E

  

- wherein

Where ,

I : Inverse

L : Logarithmic

A : Algebraic 

T : Trignometric

E : Exponential

 

 

We have Logarithmic and Algebraic Functions, We give preference to Logarithmic Function.

            0 < x < 1, |ln x| = - ln x

So, \int {|\ln x|dx} = - \left( {x\ln x - x} \right) + c = x + x|\ln x| + c


Option 1)

x\left ( \left | \ln x \right | \right )-\left ( x-1 \right )+c

Option 2)

x\left ( \left | \ln x \right | \right )-x+c

Option 3)

x\left ( \left | \ln x \right | \right )+\left ( x-1 \right )+c

Option 4)

x+x\left ( \left | \ln x \right | \right )+c

Posted by

gaurav

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