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integration of log(1+x^3)
Dear Piyush
I= ∫1* log(1+x^3) dx
intigrate by part take 1 as second function
I= x log(1+x^3) -∫3x3/(1+x^3) dx
I= x log(1+x^3) -3∫(x3 +1 -1 )/(1+x^3) dx
I= x log(1+x^3) --3x +3∫1 /(1+x^3) dx
now use partial fraction
1 /(1+x^3) = 1/3(x+1) + (2-x)/3(x2-x+1)
so intigral become
I= x log(1+x^3) --3x +∫1 /(1+x) dx + ∫2-x)/(x2-x+1) dx
now it is simple intigration
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its is frm of 1*log(1+x3) apply product rule ..take log as a 1 function and '1' as second function ....
and solve it........
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