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 2/(x^3sqrt(x^4-81))

解答

\int \frac{2}{x ^{3} x ^{4} - 81} d x

解答

\frac{x ^{4} - 81}{81 x ^{2}} + C

求解步骤

\int \frac{2}{x ^{3} x ^{4} - 81} d x

提出常数:

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

= 2 \cdot \int \frac{1}{x ^{3} x ^{4} - 81} d x

使用换元积分法

= 2 \cdot \int \frac{1}{2 u ^{2} u ^{2} - 81} d u

提出常数:

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

= 2 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{2} u ^{2} - 81} d u

使用三角换元法

= 2 \cdot \frac{1}{2} \cdot \int \frac{1}{81 sec ( v )} d v

提出常数:

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

= 2 \cdot \frac{1}{2} \cdot \frac{1}{81} \cdot \int \frac{1}{sec ( v )} d v

使用三角恒等式改写

= 2 \cdot \frac{1}{2} \cdot \frac{1}{81} \cdot \int cos (v) d v

使用积分常见定则:

\int cos (v) d v = sin (v)

= 2 \cdot \frac{1}{2} \cdot \frac{1}{81} sin (v)

代回

= 2 \cdot \frac{1}{2} \cdot \frac{1}{81} sin (arcsec (\frac{1}{9} x^{2}))

化简

2 \cdot \frac{1}{2} \cdot \frac{1}{81} sin (arcsec (\frac{1}{9} x^{2})) : \frac{x ^{4} - 81}{81 x ^{2}}

= \frac{x ^{4} - 81}{81 x ^{2}}

解答补常数

= \frac{x ^{4} - 81}{81 x ^{2}} + C

作图

流行的例子

d/(dt)(e^{-at}cos(wt))

\frac{d}{d t} (e^{- a t} cos (wt))

integral of (x^22^x+x)/(x^2)

\int \frac{x ^{2} 2 ^{x} + x}{x ^{2}} d x

derivative of ((3x^2+1^3)/((2x^2-1)^4))

\frac{d}{d x} (\frac{( 3 x ^{2} + 1 ) ^{3}}{( 2 x ^{2} - 1 ) ^{4}})

f^{^{'}} (x) = a^{2 x}

sum from n=1 to infinity of ((n-2)/n)^n

n = 1 \sum \infty (\frac{n - 2}{n})^{n}