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人気のある微分積分 >

integral of cot^2(xcs)c^4x

解

\int cot^{2} (x cs) c^{4} x d x

解

\frac{c ^{2}}{2 s ^{2}} (- c^{2} s^{2} x^{2} - 2 cs x cot (cs x) + 2 ln ∣ sin (cs x) ∣) + C

解答ステップ

\int cot^{2} (x cs) c^{4} x d x

定数を除く:

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

= c^{4} \cdot \int cot^{2} (cs x) x d x

u置換積分法を適用する

= c^{4} \cdot \int \frac{u cot ^{2} ( u )}{c ^{2} s ^{2}} d u

定数を除く:

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

= c^{4} \frac{1}{c ^{2} s ^{2}} \cdot \int u cot^{2} (u) d u

部分積分を適用する

= c^{4} \frac{1}{c ^{2} s ^{2}} (u (- u - cot (u)) - \int - u - cot (u) d u)

\int - u - cot (u) d u = - \frac{u ^{2}}{2} - ln ∣ sin (u) ∣

= c^{4} \frac{1}{c ^{2} s ^{2}} (u (- u - cot (u)) - (- \frac{u ^{2}}{2} - ln ∣ sin (u) ∣))

代用を戻す

u = cs x

= c^{4} \frac{1}{c ^{2} s ^{2}} (cs x (- cs x - cot (cs x)) - (- \frac{( cs x ) ^{2}}{2} - ln ∣ sin (cs x) ∣))

簡素化

c^{4} \frac{1}{c ^{2} s ^{2}} (cs x (- cs x - cot (cs x)) - (- \frac{( cs x ) ^{2}}{2} - ln ∣ sin (cs x) ∣)) : \frac{c ^{2}}{2 s ^{2}} (- c^{2} s^{2} x^{2} - 2 cs x cot (cs x) + 2 ln ∣ sin (cs x) ∣)

= \frac{c ^{2}}{2 s ^{2}} (- c^{2} s^{2} x^{2} - 2 cs x cot (cs x) + 2 ln ∣ sin (cs x) ∣)

定数を解答に追加する

= \frac{c ^{2}}{2 s ^{2}} (- c^{2} s^{2} x^{2} - 2 cs x cot (cs x) + 2 ln ∣ sin (cs x) ∣) + C

グラフ

人気の例

derivative of-2(x+3(x-3)^2)

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

derivative of (cos(y+2e^{-x}cos(x))/y)

\frac{d}{d x} (\frac{cos ( y ) + 2 e ^{- x} cos ( x )}{y})

tangent y=3xe^x,(0,0)

t an g e n t y = 3 x e^{x}, (0, 0)

y^{^{'}} = x y + x

\frac{d y}{d t} + 6 y = 0