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 e^{2y}(4-e^{2y})^{4/3}

解答

\int e^{2 y} (4 - e^{2 y})^{\frac{4}{3}} d y

解答

- \frac{3}{14} (4 - e^{2 y})^{\frac{7}{3}} + C

求解步骤

\int e^{2 y} (4 - e^{2 y})^{\frac{4}{3}} d y

使用换元积分法

= \int - \frac{u ^{\frac{4}{3}}}{2} d u

提出常数:

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

= - \frac{1}{2} \cdot \int u^{\frac{4}{3}} d u

使用幂法则

= - \frac{1}{2} \cdot \frac{3}{7} u^{\frac{7}{3}}

u = 4 - e^{2 y}

代回

= - \frac{1}{2} \cdot \frac{3}{7} (4 - e^{2 y})^{\frac{7}{3}}

化简

- \frac{1}{2} \cdot \frac{3}{7} (4 - e^{2 y})^{\frac{7}{3}} : - \frac{3}{14} (4 - e^{2 y})^{\frac{7}{3}}

= - \frac{3}{14} (4 - e^{2 y})^{\frac{7}{3}}

解答补常数

= - \frac{3}{14} (4 - e^{2 y})^{\frac{7}{3}} + C

作图

流行的例子

integral of (e^{y^2}y)

\int (e^{y^{2}} y) d y

integral of (-3x^2)/(sqrt(16-x^2))

\int \frac{- 3 x ^{2}}{16 - x ^{2}} d x

\int 80 d x

integral of 1/(xsqrt(49x^2-6))

\int \frac{1}{x 49 x ^{2} - 6} d x

integral of (3x^2+7x-2)/(x^3-x^2-2x)

\int \frac{3 x ^{2} + 7 x - 2}{x ^{3} - x ^{2} - 2 x} d x