不定积分,谢谢大神,求过程
1个回答
2017-08-23
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14.令x^4=t原式=1/12∫1/(x^8+3x^4+2)dx^12=1/12∫1/(t²+3t+2)dt³=1/4∫t²/(t²+3t+2)dt=1/4∫(t²+3t+2-3t-2)/(t²+3t+2)dt=1/4∫[1-(3t+3-1)/(t+1)(t+2)]dt=1/4t-3/4∫[1/(t+2)-1/(t+1)(t+2)]dt=1/4t-3/4ln|t+2|+3/4∫[1/(t+1)-1/(t+2)]dt=1/4t-3/4ln|t+2|+3/4ln|t+1|-3/4ln|t+2|+c=1/4t-3/2ln|t+2|+3/4ln|t+1|+c16.令arcsinx=tx=sint原式=∫t²dsint=t²sint-2∫tsintdt=t²sint+2∫tdcost=t²sint+2tcost-2∫costdt=t²sint+2tcost-2sint+c=x(arcsinx)²+2arcsinx·√(1-x²)-2x+c
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