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人気のある微分積分 >

integral of ((csc^2(x))/(cot^3(x)))

解

\int (\frac{csc ^{2} ( x )}{cot ^{3} ( x )}) d x

解

\frac{1}{2} tan^{2} (x) + C

解答ステップ

\int \frac{csc ^{2} ( x )}{cot ^{3} ( x )} d x

u置換積分法を適用する

= \int - \frac{1}{u ^{3}} d u

定数を除く:

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

= - \int \frac{1}{u ^{3}} d u

べき乗則を適用する

= - (- \frac{1}{2 u ^{2}})

代用を戻す

u = cot (x)

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

簡素化

- (- \frac{1}{2 cot ^{2} ( x )}) : \frac{1}{2} tan^{2} (x)

= \frac{1}{2} tan^{2} (x)

定数を解答に追加する

= \frac{1}{2} tan^{2} (x) + C

グラフ

人気の例

(dQ)/(dt)=k(Q-70)

\frac{d Q}{d t} = k (Q - 70)

derivative of-3/2 x^3+2/5 x^2-4

\frac{d}{d x} (- \frac{3}{2} x^{3} + \frac{2}{5} x^{2} - 4)

integral of 50x^3sqrt(1-25x^2)

\int 50 x^{3} 1 - 25 x^{2} d x

limit as x approaches-2 of (-3)/(2-x)

x \to - 2 lim (\frac{- 3}{2 - x})

(\partial)/(\partial x)(log_{5}(x))

\frac{\partial}{\partial x} (lo g_{5} (x))