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人気のある微分積分 >

(dy)/(dx)= x/(1+x^2)

解

\frac{d y}{d x} = \frac{x}{1 + x ^{2}}

解

y = \frac{1}{2} ln (1 + x^{2}) + c_{1}

解答ステップ

\frac{d y}{d x} = \frac{x}{1 + x ^{2}}

代用

\frac{d y}{d x}

と

y^{'} (x)

y^{^{'}} (x) = \frac{x}{1 + x ^{2}}

f^{^{'}} (x) = g (x)

であれば

f (x) = \int g (x) d x

y = \int \frac{x}{1 + x ^{2}} d x

\int \frac{x}{1 + x ^{2}} d x = \frac{1}{2} ln (1 + x^{2}) + c_{1}

y = \frac{1}{2} ln (1 + x^{2}) + c_{1}

グラフ

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