∫ x^3lnx dx
= ∫ lnx d(x^4/4)
= (1/4)x^4lnx - (1/4)∫ x^4 d(lnx)
= (1/4)x^4lnx - (1/4)∫ x^3 dx
= (1/4)x^4lnx - (1/4)(x^4/4) + C
= (1/16)(4lnx - 1)x^4 + C
∫ x^3lnx dx
= ∫ lnx d(x^4/4)
= (1/4)x^4lnx - (1/4)∫ x^4 d(lnx)
= (1/4)x^4lnx - (1/4)∫ x^3 dx
= (1/4)x^4lnx - (1/4)(x^4/4) + C
= (1/16)(4lnx - 1)x^4 + C