Question

求不定积分详细解析

Answer 1

令t=x^(1/3),即x=t³, dx=t²dt于是
原不定积分=∫(e^t)/t *t²dt
=∫(e^t) *tdt=∫td(e^t)
=t(e^t) -∫e^tdt
=t(e^t) -∫de^t
=t(e^t) -e^t + C (将 t=x^(1/3)代回)
=[x^(1/3)-1] *e^[x^(1/3)] + C