求不定積分∫（2x+1)/(x^2+2x-15)dx
求不定積分∫（2x+1)/(x^2+2x-15)dx
數(shù)學(xué)人氣：743 ℃時間：2020-04-08 07:49:04
優(yōu)質(zhì)解答
原式=∫{（2x+2）-1}/(x^2+2x-15)dx=∫（2x+2)/(x^2+2x-15)-1/(x^2+2x-15)dx=ln(x^2+2x-15)-∫1/(x-3)(x+5)dx+c=ln(x^2+2x-15)-1/8∫1/(x-3)-1/(x+5)dx+c=ln(x^2+2x-15)-1/8{ln(x-3)-ln(x+5)}+c
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