ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral of ((sec(x))/(tan(x)))^4

解

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

解

- \frac{1}{3} cot^{3} (x) - cot (x) + C

解答ステップ

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

u置換積分法を適用する

= \int \frac{1 + u ^{2}}{u ^{4}} d u

拡張

\frac{1 + u ^{2}}{u ^{4}} : \frac{1}{u ^{4}} + \frac{1}{u ^{2}}

= \int \frac{1}{u ^{4}} + \frac{1}{u ^{2}} 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 \frac{1}{u ^{4}} d u + \int \frac{1}{u ^{2}} d u

\int \frac{1}{u ^{4}} d u = - \frac{1}{3 u ^{3}}

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

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

代用を戻す

u = tan (x)

= - \frac{1}{3 tan ^{3} ( x )} - \frac{1}{tan ( x )}

簡素化

- \frac{1}{3 tan ^{3} ( x )} - \frac{1}{tan ( x )} : - \frac{1}{3} cot^{3} (x) - cot (x)

= - \frac{1}{3} cot^{3} (x) - cot (x)

定数を解答に追加する

= - \frac{1}{3} cot^{3} (x) - cot (x) + C

グラフ

人気の例

(dy)/(dx)=e^{4x-3y},y(0)=2

\frac{d y}{d x} = e^{4 x - 3 y}, y (0) = 2

integral of (sin^5(x))/(sqrt(cos(x)))

\int \frac{sin ^{5} ( x )}{cos ( x )} d x

derivative y=sqrt(\sqrt{\sqrt{x)}}

d er i v a t i v e y = x

(\partial)/(\partial s)(t^2-2s^2)

\frac{\partial}{\partial s} (t^{2} - 2 s^{2})

integral of 7t^8

\int 7 t^{8} d t