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-5tan^5(4x)sec^6(4x)

解

\int - 5 tan^{5} (4 x) sec^{6} (4 x) d x

解

- 5 (\frac{sec ^{10} ( 4 x )}{40} - \frac{sec ^{8} ( 4 x )}{16} + \frac{sec ^{6} ( 4 x )}{24}) + C

解答ステップ

\int - 5 tan^{5} (4 x) sec^{6} (4 x) d x

定数を除く:

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

= - 5 \cdot \int tan^{5} (4 x) sec^{6} (4 x) d x

三角関数の公式を使用して書き換える

= - 5 \cdot \int (- 1 + sec^{2} (4 x))^{2} tan (4 x) sec^{6} (4 x) d x

u置換積分法を適用する

= - 5 \cdot \int \frac{u ^{5} ( u ^{2} - 1 ) ^{2}}{4} d u

拡張

\frac{u ^{5} ( u ^{2} - 1 ) ^{2}}{4} : \frac{u ^{9}}{4} - \frac{u ^{7}}{2} + \frac{u ^{5}}{4}

= - 5 \cdot \int \frac{u ^{9}}{4} - \frac{u ^{7}}{2} + \frac{u ^{5}}{4} 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

= - 5 (\int \frac{u ^{9}}{4} d u - \int \frac{u ^{7}}{2} d u + \int \frac{u ^{5}}{4} d u)

\int \frac{u ^{9}}{4} d u = \frac{u ^{10}}{40}

\int \frac{u ^{7}}{2} d u = \frac{u ^{8}}{16}

\int \frac{u ^{5}}{4} d u = \frac{u ^{6}}{24}

= - 5 (\frac{u ^{10}}{40} - \frac{u ^{8}}{16} + \frac{u ^{6}}{24})

代用を戻す

u = sec (4 x)

= - 5 (\frac{sec ^{10} ( 4 x )}{40} - \frac{sec ^{8} ( 4 x )}{16} + \frac{sec ^{6} ( 4 x )}{24})

定数を解答に追加する

= - 5 (\frac{sec ^{10} ( 4 x )}{40} - \frac{sec ^{8} ( 4 x )}{16} + \frac{sec ^{6} ( 4 x )}{24}) + C

グラフ

人気の例

limit as x approaches 0 of (tan(9x))/(sin(4x))

x \to 0 lim (\frac{tan ( 9 x )}{sin ( 4 x )})

integral of x/(\sqrt[4]{x+4)}

\int \frac{x}{4 x + 4} d x

(\partial)/(\partial x)(xe^y)

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

slopeintercept (1,1),(3,-5/6)

s l o p e in t erce pt (1, 1), (3, - \frac{5}{6})

integral of sin(3x)sin(8x)

\int sin (3 x) sin (8 x) d x