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人気のある微分積分 >

integral of (arcsin(6x))/(sqrt(1-36x^2))

解

\int \frac{arcsin ( 6 x )}{1 - 36 x ^{2}} d x

解

\frac{1}{12} arcsin^{2} (6 x) + C

解答ステップ

\int \frac{arcsin ( 6 x )}{1 - 36 x ^{2}} d x

u置換積分法を適用する

= \int \frac{arcsin ( u )}{6 1 - u ^{2}} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int \frac{arcsin ( u )}{1 - u ^{2}} d u

u置換積分法を適用する

= \frac{1}{6} \cdot \int v d v

べき乗則を適用する

= \frac{1}{6} \cdot \frac{v ^{2}}{2}

代用を戻す

= \frac{1}{6} \cdot \frac{arcsin ^{2} ( 6 x )}{2}

簡素化

\frac{1}{6} \cdot \frac{arcsin ^{2} ( 6 x )}{2} : \frac{1}{12} arcsin^{2} (6 x)

= \frac{1}{12} arcsin^{2} (6 x)

定数を解答に追加する

= \frac{1}{12} arcsin^{2} (6 x) + C

グラフ

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