求不定积分，高等数学，过程！

Question

如题所述

Answer 1

1、令x=t^6，dx=6t^5dt
原式=∫6t^5dt/(t^3+t^2)
=6*∫t^3dt/(t+1)
=6*∫[(t^3+1)/(t+1)-1/(t+1)]dt
=6*∫[t^2-t+1-1/(t+1)]dt
=6*[t^3/3-t^2/2+t-ln|t+1|]+C
=2t^3-3t^2+6t-6ln|t+1|+C
=2x^(1/2)-3x^(1/3)+6x^(1/6)-6ln|x^(1/6)+1|+C，其中C是任意常数
2、原式=∫2x/√(1-x^2)dx-∫1/√(1-x^2)dx
=-∫d(1-x^2)/√(1-x^2)-arcsinx
=-2√(1-x^2)-arcsinx+C，其中C是任意常数

Answer 2

追答

Answer 3

追答

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