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¹p»ç系 }(100ç ˇ) Àj 26 }¶ } 單元 26 分部積分 (}$˜í乘¶d†)({ §72)q u = u(x), v = v(x) ÌÑ x íª 函b, †根W乘 ¶d† (uv)0 = u0v uv0 â¤û uv0 = (uv)0 − u0v si },) Z uv0 dx = Z (uv)0 dx − Z u0vdx ÄÑ uv u (uv)0 íø¥û函b, Z uv0dx = uv − Z u0vdx (1) I }˜ du = u0dx J£ dv = v0dx † (1) ˜óçk Z udv = uv − Z vdu ¤4另ø }x巧, ˚TDec 09, 07 · ∫x dx/(x^2 1) = (1/2)∫2x dx/(x^2 1) と考えれば、即刻積分でき、 ∫x dx/(x^2 1) = (1/2)∫2x dx/(x^2 1) = (1/2) {ln (x^2 1)} C 慣れていなければ、 x^2 = t と置けば、 dt/dx = 2x dx = dt/(2x) だから、 ∫x dx/(x^2 1) = ∫dt/{2 (t 1)} = (1/2)∫dt/(t 1) = (1/2) (ln t 1) C t を戻せば、絶対値の中身は常に正だから、 (1/2) ln t 1 C = (1/2) ln (x^2 1) C 以上より ∫x dx/(x^2 1) =\int \frac{1}{x^2}dx zs Related Symbolab blog posts Advanced Math Solutions – Integral Calculator, integration by parts, Part II In the previous post we covered integration by parts Quick review Integration by parts is essentially the reverse 1 X 4 1 積分 史丹利的數學世界 X/1+x^2 積分 無限