If dx/x( x-2)( x-3) = I + C, then I isequal to

Correct Answer is : log⁡∣log⁡x−3log⁡x−2∣ ≤ft| x-3/ x-2 |loglogx−2logx−3

Correct Answer is : log⁡∣log⁡x−3log⁡x−2∣ ≤ft| x-3/ x-2 |loglogx−2logx−3

Test Index

AP EAMCET Engineering 2013 Solved Paper

Section: Mathematics

Question : 155 of 160

Marks: +1, -0

\int \frac{dx}{x(\log x-2)(\log x-3)} = I + C

I

isequal to

Solution:

Let

l_{1} = \int \frac{dx}{x(\log x-2)(\log x-3)}

Let

t = \log x \Rightarrow dt = \frac{dx}{x}

∴

l_{1} = \int \frac{dt}{(t-2)(t-3)}

= \int \left[ \frac{1}{(t-3)} - \frac{1}{(t-2)} \right] dt

= \log |(t-3)| - \log |(t-2)| + C

= \log \left| \frac{\log x-3}{\log x-2} \right| + C

⇒

I_{1} = \int \frac{dx}{x(\log x-2)(\log x-3)}

= \log \left| \frac{\log x-3}{\log x-2} \right| + C

But given,

\int \frac{dx}{x(\log x-2)(\log x-3)} = I + C

On comparing, we get

I = \log \left| \frac{\log x-3}{\log x-2} \right|

Go to Question:

Prev Question

Next Question