فرمول های انتگرال (Integral) شامل عبارت $ {a^2} + {x^2} $ ، در ریاضیات (Mathematics)
\[ \int {{1 \over {{a^2} + {x^2}}}dx} = {1 \over a}{\tan ^{ - 1}}{x \over a} + C
\]
\[ \int {{1 \over {{{({a^2} + {x^2})}^2}}}dx} = {x \over {2{a^2}({a^2} + {x^2})}} + {1 \over {2{a^3}}}{\tan ^{ - 1}}{x \over a} + C
\]
\[ \int {{1 \over {\sqrt {{a^2} + {x^2}} }}dx} = {\sinh ^{ - 1}}{x \over a} + C = \ln \left( {x + \sqrt {{a^2} + {x^2}} } \right) + C
\]
\[ \int {\sqrt {{a^2} + {x^2}} } dx = {x \over 2}\sqrt {{a^2} + {x^2}} + {{{a^2}} \over 2}\ln \left( {x + \sqrt {{a^2} + {x^2}} } \right) + C
\]
\[ \int {{x^2}} \sqrt {{a^2} + {x^2}} dx = {x \over 8}({a^2} + 2{x^2})\sqrt {{a^2} + {x^2}} - {{{a^4}} \over 8}\ln (x + \sqrt {{a^2} + {x^2}} ) + C
\]
\[ \int {{{\sqrt {{a^2} + {x^2}} } \over x}} dx = \sqrt {{a^2} + {x^2}} - a\ln \left| {{{a + \sqrt {{a^2} + {x^2}} } \over x}} \right| + C
\]
\[ \int {{{\sqrt {{a^2} + {x^2}} } \over {{x^2}}}} dx = \ln (x + \sqrt {{a^2} + {x^2}} ) - {{\sqrt {{a^2} + {x^2}} } \over x} + C
\]
\[ \int {{{{x^2}} \over {\sqrt {{a^2} + {x^2}} }}} dx = - {{{a^2}} \over 2}\ln (x + \sqrt {{a^2} + {x^2}} ) + {{x\sqrt {{a^2} + {x^2}} } \over 2} + C
\]
\[ \int {{1 \over {x\sqrt {{a^2} + {x^2}} }}dx} = - {1 \over a}\ln \left| {{{a + \sqrt {{a^2} + {x^2}} } \over x}} \right| + C
\]
\[ \int {{1 \over {{x^2}\sqrt {{a^2} + {x^2}} }}dx} = - {{\sqrt {{a^2} + {x^2}} } \over {{a^2}x}} + C
\]
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Thomas' Calculus Early Transcendentals - George B. Thomas Jr., Maurice D. Weir, Joel R. Hass - 13th Edition
نویسنده
علیرضا گلمکانی
شماره کلید
20012
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