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@campbel2525

微分・積分公式集

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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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