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人気のある微分積分 >

integral of e^{cot(x)}cot^2(x)csc^2(x)

解

\int e^{c o t (x)} cot^{2} (x) csc^{2} (x) d x

解

- e^{c o t (x)} cot^{2} (x) + 2 e^{c o t (x)} cot (x) - 2 e^{c o t (x)} + C

解答ステップ

\int e^{c o t (x)} cot^{2} (x) csc^{2} (x) d x

u置換積分法を適用する

= \int - e^{u} u^{2} d u

定数を除く:

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

= - \int e^{u} u^{2} d u

部分積分を適用する

= - (u^{2} e^{u} - \int 2 u e^{u} d u)

\int 2 u e^{u} d u = 2 (e^{u} u - e^{u})

= - (u^{2} e^{u} - 2 (e^{u} u - e^{u}))

代用を戻す

u = cot (x)

= - (cot^{2} (x) e^{c o t (x)} - 2 (e^{c o t (x)} cot (x) - e^{c o t (x)}))

簡素化

- (cot^{2} (x) e^{c o t (x)} - 2 (e^{c o t (x)} cot (x) - e^{c o t (x)})) : - e^{c o t (x)} cot^{2} (x) + 2 e^{c o t (x)} cot (x) - 2 e^{c o t (x)}

= - e^{c o t (x)} cot^{2} (x) + 2 e^{c o t (x)} cot (x) - 2 e^{c o t (x)}

定数を解答に追加する

= - e^{c o t (x)} cot^{2} (x) + 2 e^{c o t (x)} cot (x) - 2 e^{c o t (x)} + C

グラフ

人気の例

integral of-(10)/x

\int - \frac{10}{x} d x

integral of 4/(xsqrt(x^2-16))

\int \frac{4}{x x ^{2} - 16} d x

integral of (sin^2(3x)+cos(3x))^2

\int (sin^{2} (3 x) + cos (3 x))^{2} d x

integral of (5× 2^x)/(3^x)

\int \frac{5 \times 2 ^{x}}{3 ^{x}} d x

integral of 1/(x(x+1)(x^2+x+1))

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