integral using substitution and then integration by parts
integral of [1 / (x^4)][sqrt( 1 + (x^2))][ log( 1 + (x^2)) - 2log( x)]
first simplify using property of logarithms
take x^2 common from the sqrt term obtain [1+1/(x^2)] and try to get the same term inside the log expression
cancel off the x to get 1 /[x^3] then use substitution
then use integration by parts with log(t) as the first function
formulae on integration
PAGE 1 BASIC INTEGRATION
PAGE 2 INTEGRATION BY SUBSTITUTION
PAGE 3 INTEGRATION BY COMPLETION OF SQUARES
PAGE 4 INTEGRATION BY PARTS
PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR
PAGE 6 INTEGRATION USING PARTIAL FRACTIONS
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