ज्ञात करें `int (x^2)/((1+x^3)(2+x^3))dx`

Explanation

माना की `I = int x^2/((1+x^3)(2+x^3)) dx`
`x^3 =t ` रखे, तो `x^2 dx = 1/3 dt `
`:." "I = 1/3 int (dt)/((1+t)(2+t)) = 1/3 int [1/(1+t)-1/(2+t)]dt` [ partial fraction से ]
`=1/3 [ log | 1 + t | - log | 2+t|] +c =1/3 log |(1+x^3)/(2+x^3)|+c`