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3.
令√x=t,则x=t²
∫[(1+x)²/√x]dx
= ∫[(1+t²)²/t]d(t²)
=2∫[(1+t²)²·t/t]dt
=2∫(t⁴+2t²+1)dt
=2[(1/5)t⁵+(2/3)t³+t] +C
=(2/15)(3t⁴+10t²+15)t +C
=(2/15)(3x²+10x+15)√x +C
令√x=t,则x=t²
∫[(1+x)²/√x]dx
= ∫[(1+t²)²/t]d(t²)
=2∫[(1+t²)²·t/t]dt
=2∫(t⁴+2t²+1)dt
=2[(1/5)t⁵+(2/3)t³+t] +C
=(2/15)(3t⁴+10t²+15)t +C
=(2/15)(3x²+10x+15)√x +C
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