`intx^(2)e^(x^(3))dx=?`

Options

A. `(1)/(3)e^(x^(3))+C`
B. `(1)/(3)e^(x^(2))+C`
C. `(1)/(2)e^(x^(3))+C`
D. `(1)/(2)e^(x^(2))+C`

Answer

A

Explanation

माना `I=intx^(2)e^(x^(3))dx`
माना `x^(3)=t" "rArr" "3x^(2)dx=dt" "rArr" "x^(2)dx=(dt)/(3)`
`therefore" "I=(1)/(3)inte^(t)dt" "rArr" "I=(1)/(3)e^(t)+C=(1)/(3)e^(x^(3))+C`