设x=t的6次方
∴t=6次根号下t
∫1/(t³+t²）dt的6次方
=∫6t的5次方/t²(t+1) dt
=∫6t³/(t+1)dt
=6∫(t³+1-1)/(t+1)dt
=6∫[t²-t+1 -1/(t+1)]dt
=6(t³/3-t²/2+t-ln|t+1|) +C
=2t³-3t²+6t-6ln|t+1|+C
=2√x-3(3次根号下x)+6(6次根号下x)-6ln(6次根号下x +1) +C
设x=t的6次方
∴t=6次根号下t
∫1/(t³+t²）dt的6次方
=∫6t的5次方/t²(t+1) dt
=∫6t³/(t+1)dt
=6∫(t³+1-1)/(t+1)dt
=6∫[t²-t+1 -1/(t+1)]dt
=6(t³/3-t²/2+t-ln|t+1|) +C
=2t³-3t²+6t-6ln|t+1|+C
=2√x-3(3次根号下x)+6(6次根号下x)-6ln(6次根号下x +1) +C