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# integration of log(1+x^3)

147 Points
11 years ago

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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yogesh gandhi
8 Points
11 years ago

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........