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 8/(t^9)sin(1/(t^8)-9)

解答

\int \frac{8}{t ^{9}} sin (\frac{1}{t ^{8}} - 9) d t

解答

cos (\frac{1}{t ^{8}} - 9) + C

求解步骤

\int \frac{8}{t ^{9}} sin (\frac{1}{t ^{8}} - 9) d t

提出常数:

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

= 8 \cdot \int \frac{1}{t ^{9}} sin (\frac{1}{t ^{8}} - 9) d t

使用换元积分法

= 8 \cdot \int - \frac{sin ( u )}{8} d u

提出常数:

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

= 8 (- \frac{1}{8} \cdot \int sin (u) d u)

使用积分常见定则:

\int sin (u) d u = - cos (u)

= 8 (- \frac{1}{8} (- cos (u)))

u = \frac{1}{t ^{8}} - 9

代回

= 8 (- \frac{1}{8} (- cos (\frac{1}{t ^{8}} - 9)))

化简

8 (- \frac{1}{8} (- cos (\frac{1}{t ^{8}} - 9))) : cos (\frac{1}{t ^{8}} - 9)

= cos (\frac{1}{t ^{8}} - 9)

解答补常数

= cos (\frac{1}{t ^{8}} - 9) + C

作图

流行的例子

y^'+tan(x)y=cos^2(x)

y^{^{'}} + tan (x) y = cos^{2} (x)

(\partial)/(\partial x)(tan(2x-y))

\frac{\partial}{\partial x} (tan (2 x - y))

(\partial)/(\partial x)((x^2-2)e^{x^2y})

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

integral of (30)/(30+e^x)

\int \frac{30}{30 + e ^{x}} d x

derivative y=4(6-x^2)^5

d er i v a t i v e y = 4 (6 - x^{2})^{5}