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人気のある微分積分 >

integral of 6x*csc^2(8x^2)

解

\int 6 x \cdot csc^{2} (8 x^{2}) d x

解

- \frac{3}{8} cot (8 x^{2}) + C

解答ステップ

\int 6 x csc^{2} (8 x^{2}) d x

定数を除く:

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

= 6 \cdot \int x csc^{2} (8 x^{2}) d x

u置換積分法を適用する

= 6 \cdot \int \frac{csc ^{2} ( 8 u )}{2} d u

定数を除く:

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

= 6 \cdot \frac{1}{2} \cdot \int csc^{2} (8 u) d u

u置換積分法を適用する

= 6 \cdot \frac{1}{2} \cdot \int csc^{2} (v) \frac{1}{8} d v

定数を除く:

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

= 6 \cdot \frac{1}{2} \cdot \frac{1}{8} \cdot \int csc^{2} (v) d v

共通積分を使用する:

\int csc^{2} (v) d v = - cot (v)

= 6 \cdot \frac{1}{2} \cdot \frac{1}{8} (- cot (v))

代用を戻す

= 6 \cdot \frac{1}{2} \cdot \frac{1}{8} (- cot (8 x^{2}))

簡素化

6 \cdot \frac{1}{2} \cdot \frac{1}{8} (- cot (8 x^{2})) : - \frac{3}{8} cot (8 x^{2})

= - \frac{3}{8} cot (8 x^{2})

定数を解答に追加する

= - \frac{3}{8} cot (8 x^{2}) + C

グラフ

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