Jawapan:
# 1/6 ln | {sqrt (x ^ 3 + 4) -2} / {sqrt (x ^ 3 + 4) +2} | + C #
Penjelasan:
Pengganti # x ^ 3 + 4 = u ^ 2 #. Kemudian # 3x ^ 2dx = 2udu #, jadi
# dx / {x sqrt {x ^ 3 + 4}} = {2udu} / {3x ^ 3u} = 2/3 {du} / (u ^ 2-4) = 1/6 ({du} / {u -2} - {du} / {u + 2}) #
Oleh itu
#int dx / {x sqrt {x ^ 3 + 4}} = 1/6 int ({du} / {u-2} - {du} / {u + 2}) = 1/6 ln | {u- 2} / {u + 2} | + C #
# = 1/6 ln | {sqrt (x ^ 3 + 4) -2} / {sqrt (x ^ 3 + 4) +2} | + C #
