Question

Friends I am preparing for nest help me in this question

find the integration of ∫[ ln ( ln(x) + 1/(ln(x)^2 ]dx

Answer 1

hello pari  :-) 

our question is  ∫[ ln ( ln(x) + 1/(ln(x)^2 ]dx 

now we let ln(x) = > t 

we get x = > e^t 

we get dx = > e^t 

∫ [ lnt + 1/t² ] e^t dt 

solving this we get 

∫e^t [ ln (t) - 1/t  + 1/t  +1 /t ²         i did this to reduce this function : = ) 

 ln (t) - 1/t  be g(x)    1/t  +1 /t ²   = > g·(x)  

we get   e^t [ ln(t)  -1/t ] + C  

Hopes this will help you pari  ! 

@ gopal khandelwal b-tec from IIT ROORKEY