\u8b1b\u7fa9\u5185\u3067\u306f\u8a08\u7b97\u904e\u7a0b\u3092\u7701\u7565\u3057\u305f\u306e\u3067\u3001\u3053\u3053\u306b\u63b2\u8f09\u3057\u307e\u3059\u3002<\/p>\n
\\begin{eqnarray}
\n\\displaystyle \\int_{-\\infty}^{\\infty} \\frac{1}{(z^2 +a^2)^{\\frac{3}{2}}}dz = \\frac{2}{a^2}
\n\\end{eqnarray}<\/p>\n
\u3053\u306e\u7a4d\u5206\u306f$\\ z=a \\tan x$\u3068\u7f6e\u63db\u3092\u3057\u3066\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n
\u4e0b\u6e96\u5099<\/p>\n
\\begin{eqnarray}
\nz &=& a \\tan x \\\\
\ndz &=& a \\frac{1}{\\cos^2 x} dx \\\\
\n\\end{eqnarray}<\/p>\n
\u307e\u305f\u3001\u4e09\u89d2\u95a2\u6570\u306e\u95a2\u4fc2\u5f0f$\\ \\tan^2 x +1 = \\displaystyle \\frac{1}{\\cos^2 x}$\u3082\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n
\\begin{eqnarray}
\n\\displaystyle \\int_{-\\infty}^{\\infty} \\frac{1}{(z^2 +a^2)^{\\frac{3}{2}}}dz
\n&=& \\int_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}} \\frac{\\displaystyle \\frac{a}{\\cos^2 x} dx}
\n{[(a \\tan x)^2 +a^2]^{\\frac{3}{2}}}\\\\
\n& & \\\\
\n&=& \\int_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}} \\frac{\\displaystyle \\frac{a}{\\cos^2 x} dx}
\n{[a^2 (\\tan^2 x+1) ]^{\\frac{3}{2}}}\\\\
\n& & \\\\
\n&=& \\int_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}} \\frac{\\displaystyle \\frac{a}{\\cos^2 x} dx}
\n{\\left(a^2 \\displaystyle \\frac{1}{\\cos^2 x} \\right)^{\\frac{3}{2}}}\\\\
\n& & \\\\
\n&=& \\int_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}} \\frac{\\displaystyle \\frac{a}{\\cos^2 x} dx}
\n{\\displaystyle \\frac{a^3}{\\cos^3 x}}\\\\
\n\\\\
\n&=& \\frac{1}{a^2} \\int_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}} \\cos x\\ dx \\\\
\n\\\\
\n&=& \\frac{1}{a^2} \\left[ \\sin x \\right]_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}}\\\\
\n\\\\
\n&=& \\frac{1}{a^2} \\left[ \\sin \\frac{\\pi}{2} -\\sin \\left(-\\frac{\\pi}{2}\\right) \\right]\\\\
\n\\\\
\n&=&\\frac{2}{a^2}
\n\\end{eqnarray}<\/p>\n","protected":false},"excerpt":{"rendered":"
\u8b1b\u7fa9\u5185\u3067\u306f\u8a08\u7b97\u904e\u7a0b\u3092\u7701\u7565\u3057\u305f\u306e\u3067\u3001\u3053\u3053\u306b\u63b2\u8f09\u3057\u307e\u3059\u3002 \\begin{eqnarray} \\displaystyle \\int_{-\\infty}^{\\infty} \\frac{1}{(z^2 +a^2 … <\/p>\n","protected":false},"author":1,"featured_media":817,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[4,11],"tags":[],"_links":{"self":[{"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/posts\/911"}],"collection":[{"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/comments?post=911"}],"version-history":[{"count":7,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/posts\/911\/revisions"}],"predecessor-version":[{"id":918,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/posts\/911\/revisions\/918"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/media\/817"}],"wp:attachment":[{"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/media?parent=911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/categories?post=911"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/tags?post=911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}