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Piyush Prasad Grade: 12
        

integration of log(1+x^3)

7 years ago

Answers : (2)

Badiuddin askIITians.ismu Expert
147 Points
										

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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Badiuddin


 

7 years ago
yogesh gandhi
8 Points
										

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........

7 years ago
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