∫(1/x + 3/x2 - 4/x3 ) dx
⇒∫(1x+3x2−4x3)dx\Rightarrow \int(\dfrac{1}{x} + \dfrac{3}{x^2} -\dfrac{4}{x^3})dx⇒∫(x1+x23−x34)dx
⇒∫(x−1+3x−2−4x−3)dx\Rightarrow \int( x^{-1} +3 x^{-2}-4x^{-3})dx⇒∫(x−1+3x−2−4x−3)dx
⇒ln∣x∣+3x−2+1(−2+1)−4x−3+1(−3+1)\Rightarrow ln | x|+3 \dfrac{x^{-2+1}}{(-2+1)} -4 \dfrac{x^{-3+1}}{(-3+1)}⇒ln∣x∣+3(−2+1)x−2+1−4(−3+1)x−3+1
⇒ln∣x∣−3x+2x2\Rightarrow ln |x| -\dfrac{3}{x} + \dfrac{2}{x^2}⇒ln∣x∣−x3+x22
