`int(x^(2)tan^(-1)x^(3))/(1+x^(6))` का मान ज्ञात कीजिए ।

Explanation

माना `I=int(x^(2).tan^(-1)x^(3))/(1+x^(6))dx`
`" "=int tan^(-1)x^(3).((x^(2)dx)/(1+x^(6)))`
माना `tan^(-1)x^(3)=t`
`rArr" "(1)/(1+x^(6)).3x^(2)=(dt)/(dx)`
`rArr" "(x^(2)dx)/(1+x^(6))=(dt)/(3)` ltBrgt `therefore" "I=intt.(dt)/(3)=(1)/(6)t^(2)+c`
`" "=(1)/(6)(tan^(-1)x^(3))^(2)+c`