t^5/(1+t^2)的积分

题目详情

t^5/(1+t^2)的积分

▼优质解答

答案和解析

∫t^5/(1+t^2)dt
=1/2∫t^4/(1+t^2)dt^2
=1/2∫[(t^4-1+1)/(1+t^2)]dt^2
=1/2∫[t^2-1+1/(1+t^2)]dt^2
=1/4t^4-1/2t^2+1/2ln(1+t^2)+C

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