ज्ञात करें `int x^3 e^(x^(2))dx`

Explanation

माना की `x^2 =z` तो `2x dx = dz`
अब, `I = int x^3 e^(x^(2)) dx = int x^2 x dx`
`= int ze^z(dz)/2 = 1/2 ze^2 dz = 1/2 [ze^z - int (1*e^z) dz]`
`= 1/2 ze^2 - 1/2""e^z+c = 1/2 x^2 e^(x^(2)) -1/2 e^(x^(2))+c`
`=1/2 ze^(z)-1/2 e^(z)+c =1/2 x^2 e^(x^(2))+c`