1.
∫(1/x²)·e^(1/x) dx
=∫-e^(1/x) d(1/x)
=-e^(1/x) +C
2.
令√x=t,则x=t²
∫[e^(√x) /√x]dx
=∫e^t /t d(t²)
=∫e^t·2t/t dt
=∫2e^t dt
=2e^t +C
=2e^(√x) +C
3.
∫sin³xdx
=∫-sin²x d(cosx)
=∫(cos²x -1)d(cosx)
=(1/3)cos³x -cosx +C
4.
∫(arcsinx)²/√(1-x²) dx
=∫(arcsinx)² d(arcsinx)
=(1/3)(arcsinx)³ +C