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@campbel2525

微分・積分公式集

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シリーズ

物理・数学・プログラムのページについて

概要

微分積分の公式集です。よかったら活用してください。

公式

    ({\sin^{-1}x})' = \frac{ 1 }{ \sqrt{ 1 - x^2 } }
    ({\cos^{-1}x})' = \frac{ -1 }{ \sqrt{ 1 - x^2 } }
    ({\tan^{-1}x})' = \frac{ 1 }{ 1 + x^2 }
    ({\sec^{-1}x})' = \frac{ 1 }{ \vert x \vert\sqrt{ x^2 - 1 } }
    ({\csc^{-1}x})' = \frac{ -1 }{ \vert x \vert\sqrt{ x^2 - 1 } }
    ({\cot^{-1}x})' = \frac{ -1 }{ 1 + x^2 }
    ({\sinh^{-1}x})' = (log(x + \sqrt{ x^2 + 1 }))' =  \frac{ 1 }{ \sqrt{ x^2 + 1 } }
    ({\cosh^{-1}x})' = (log(x + \sqrt{ x^2 - 1 }))' =  \frac{ 1 }{ \sqrt{ x^2 - 1 } }
    ({\tanh^{-1}x})' = \frac{ 1 }{ 1 - x^2 }
    \int \sqrt{ x^2 + A }dx = \frac{ 1 }{ 2 } x\sqrt{ x^2 + A } + A\log(\vert x \vert + \sqrt{ x^2 + A })
    \int \sqrt{ a^2 - x^2 }dx = \frac{ 1 }{ 2 } x\sqrt{ a^2 - x^2} + a^2{\sin^{-1}\frac{ x }{ a }}
    \int \sqrt{ a^2 - x^2 }dx = \frac{ 1 }{ 2 } x\sqrt{ a^2 - x^2} + a^2{\sin^{-1}\frac{ x }{ a }}
    \int e^{ax}\sin bx dx = \frac{ e^{ax} }{ \sqrt{ a^2 + b^2 } }(a\sin bx - b\cos abx)
    \int e^{ax}\cos bx dx = \frac{ e^{ax} }{ \sqrt{ a^2 + b^2 } }(a\sin bx + b\cos bx)
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campbel2525
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