integration using "by parts " rule

evaluate ∫ { lnx / [x^4]} dx

take lnx as the first function

∫ { lnx / [x^4]} dx = ∫{lnx} { 1 / [x^4]} dx

= {lnx} {-1 /[ 3 x ³] } - ∫ {1/x}{-1 /[ 3 x ³] } dx

= {-lnx /[ 3 x ³] } - ∫ {-1 /[3 [x^4]] } dx

= {-lnx /[ 3 x ³] } + {-1 /[9 x³] } + C

= {-1/[ 3 x ³] } { lnx + (1/3) } +C



formulae for integration

another example on integration by parts


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