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 (3x^4)/(sqrt(1-12x^5))

解答

\int \frac{3 x ^{4}}{1 - 12 x ^{5}} d x

解答

- \frac{1}{10} 1 - 12 x^{5} + C

求解步骤

\int \frac{3 x ^{4}}{1 - 12 x ^{5}} d x

提出常数:

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

= 3 \cdot \int \frac{x ^{4}}{1 - 12 x ^{5}} d x

使用换元积分法

= 3 \cdot \int - \frac{1}{60 u} d u

提出常数:

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

= 3 (- \frac{1}{60} \cdot \int \frac{1}{u} d u)

使用幂法则

= 3 (- \frac{1}{60} \cdot 2 u^{\frac{1}{2}})

u = 1 - 12 x^{5}

代回

= 3 (- \frac{1}{60} \cdot 2 (1 - 12 x^{5})^{\frac{1}{2}})

化简

3 (- \frac{1}{60} \cdot 2 (1 - 12 x^{5})^{\frac{1}{2}}) : - \frac{1}{10} 1 - 12 x^{5}

= - \frac{1}{10} 1 - 12 x^{5}

解答补常数

= - \frac{1}{10} 1 - 12 x^{5} + C

作图

流行的例子

integral of-7/(4tsqrt(16t^2-36))

\int - \frac{7}{4 t 16 t ^{2} - 36} d t

integral of (sqrt(36-x^2))

\int (36 - x^{2}) d x

integral of 2*3^x

\int 2 \cdot 3^{x} d x

integral of 2te^{t^2-1}

\int 2 t e^{t^{2} - 1} d t

integral of ((x^2))/(x+4)

\int \frac{( x ^{2} )}{x + 4} d x