3.4 有理関数の積分法

1.

(a) $${\log{\vert x-2\vert} - \log{\vert x+5\vert}}$$(b) $${-\log{\vert x\vert} + \log\vert x^2 -1\vert}$$

(c) $${x + 7\log{\vert x-2\vert} -4 \log\vert x-1\vert}$$(d) $${\frac{3}{4}\log\vert x-1\vert - \frac{1}{2}(x-1)^{-1} + \frac{1}{4}\log\vert x+1\vert}$$

(e) $${\frac{1}{128}[\frac{4x}{\left( 16 + {x^2} \right)} - \tan^{-1} (\frac{4}{x})]}$$

(f) $${\frac{x^{4}}{4} + \frac{4x^{3}}{3} + 6x^{2} + 32x + 80\log{\vert x-2\vert} - \frac{32}{x-2}}$$

(g) $${\frac{1}{9}\log\vert x^3 -1\vert - \frac{1}{18}[\log\vert x^6 + x^3 + 1\vert + 2\sqrt{3} \tan^{-1}{(\frac{2x^3+1}{\sqrt{3}})}]}$$

(h) $${\frac{1}{4}\log{(\frac{x^4}{x^4 + 1})}}$$