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求arcsinx*e^arcsinx/根下(1-x^2)的不定积分
人气:172 ℃ 时间:2020-01-29 21:22:05
解答
∫arcsinx*e^arcsinx/√(1-x^2)dx
=∫arcsinx*e^arcsinxdarcsinx
令t=arcsinx得:
=∫te^tdt
=∫tde^t
=t*e^t-∫e^tdt
=t*e^t-e^t+C
=arcsinx*e^arcsinx-e^arcsinx+C
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