求不定积分∫(2x+1)/(x^2+2x-15)dx

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求不定积分∫(2x+1)/(x^2+2x-15)dx求不定积分∫(2x+1)/(x^2+2x-15)dx求不定积分∫(2x+1)/(x^2+2x-15)dx原式=∫{(2x+2)-1}/(x^2+2x

求不定积分∫(2x+1)/(x^2+2x-15)dx
求不定积分∫(2x+1)/(x^2+2x-15)dx

求不定积分∫(2x+1)/(x^2+2x-15)dx
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