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 tan^6(x)

解

\int tan^{6} (x) d x

解

\frac{tan ^{5} ( x )}{5} - \frac{tan ^{3} ( x )}{3} + tan (x) - arctan (tan (x)) + C

解答ステップ

\int tan^{6} (x) d x

u置換積分法を適用する

= \int \frac{u ^{6}}{1 + u ^{2}} d u

長除法

\frac{u ^{6}}{1 + u ^{2}} : u^{4} - u^{2} + 1 - \frac{1}{u ^{2} + 1}

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

\int u^{4} d u = \frac{u ^{5}}{5}

\int u^{2} d u = \frac{u ^{3}}{3}

\int 1 d u = u

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

= \frac{u ^{5}}{5} - \frac{u ^{3}}{3} + u - arctan (u)

代用を戻す

u = tan (x)

= \frac{tan ^{5} ( x )}{5} - \frac{tan ^{3} ( x )}{3} + tan (x) - arctan (tan (x))

定数を解答に追加する

= \frac{tan ^{5} ( x )}{5} - \frac{tan ^{3} ( x )}{3} + tan (x) - arctan (tan (x)) + C

グラフ

人気の例

integral from 1 to 32 of x^{-11/5}

\int_{1}^{32} x^{- \frac{11}{5}} d x

limit as x approaches-1 of (6+4x)^{2x}

x \to - 1 lim ((6 + 4 x)^{2 x})

tangent y= x/(sqrt(16x+x^2))

t an g e n t y = \frac{x}{16 x + x ^{2}}

integral of x^{16}e^{x^{17}}

\int x^{16} e^{x^{17}} d x

(\partial)/(\partial x)(e^{7x})

\frac{\partial}{\partial x} (e^{7 x})