zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

integral of tan^5(6x)sec^2(6x)

解答

\int tan^{5} (6 x) sec^{2} (6 x) d x

解答

\frac{1}{36} tan^{6} (6 x) + C

求解步骤

\int tan^{5} (6 x) sec^{2} (6 x) d x

使用换元积分法

= \int tan^{5} (u) sec^{2} (u) \frac{1}{6} d u

提出常数:

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

= \frac{1}{6} \cdot \int tan^{5} (u) sec^{2} (u) d u

使用三角恒等式改写

= \frac{1}{6} \cdot \int (1 + tan^{2} (u)) tan^{5} (u) d u

使用换元积分法

= \frac{1}{6} \cdot \int v^{5} d v

使用幂法则

= \frac{1}{6} \cdot \frac{v ^{6}}{6}

代回

= \frac{1}{6} \cdot \frac{tan ^{6} ( 6 x )}{6}

化简

\frac{1}{6} \cdot \frac{tan ^{6} ( 6 x )}{6} : \frac{1}{36} tan^{6} (6 x)

= \frac{1}{36} tan^{6} (6 x)

解答补常数

= \frac{1}{36} tan^{6} (6 x) + C

作图

流行的例子

derivative of 1/(9x^{8/9})

\frac{d}{d x} (\frac{1}{9 x ^{\frac{8}{9}}})

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

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

(\partial)/(\partial x)(7-x^2+xy-2y^2)

\frac{\partial}{\partial x} (7 - x^{2} + x y - 2 y^{2})

derivative of 6x^{-2}

\frac{d}{d x} (6 x^{- 2})

tangent 4x-x^2,(1.3)

t an g e n t 4 x - x^{2}, (1.3)