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人気のある微分積分 >

integral of (sec^4(t))/(tan^2(t))

解

\int \frac{sec ^{4} ( t )}{tan ^{2} ( t )} d t

解

- 2 cot (2 t) + C

解答ステップ

\int \frac{sec ^{4} ( t )}{tan ^{2} ( t )} d t

u置換積分法を適用する

= \int \frac{1 + u ^{2}}{u ^{2}} d u

\frac{1 + u ^{2}}{u ^{2}} = \frac{1}{u ^{2}} + 1

= \int \frac{1}{u ^{2}} + 1 d u

指数の規則を適用する:

\frac{1}{a ^{b}} = a^{- b}

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

= \int u^{- 2} + 1 d u

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{- 2} d u + \int 1 d u

\int u^{- 2} d u = - \frac{1}{u}

\int 1 d u = u

= - \frac{1}{u} + u

代用を戻す

u = tan (t)

= - \frac{1}{tan ( t )} + tan (t)

簡素化

- \frac{1}{tan ( t )} + tan (t) : - 2 cot (2 t)

= - 2 cot (2 t)

定数を解答に追加する

= - 2 cot (2 t) + C

グラフ

人気の例

derivative of (x^2+2x/(4-5x))

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

tangent f(x)=tan(x),\at x= pi/4

t an g e n t f (x) = tan (x), at x = \frac{π}{4}

limit as x approaches 0 of (cos(7x)tan(7x))/x

x \to 0 lim (\frac{cos ( 7 x ) tan ( 7 x )}{x})

(\partial)/(\partial y)(e^{xy})

\frac{\partial}{\partial y} (e^{x y})

limit as x approaches 3 of ((x^4-81))/(x-3)

x \to 3 lim (\frac{( x ^{4} - 81 )}{x - 3})