ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral of (2xln(x))/(-x^4)

解

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

解

\frac{ln ( x )}{x ^{2}} + \frac{1}{2 x ^{2}} + C

解答ステップ

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

定数を除く:

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

= \frac{2}{- 1} \cdot \int \frac{x ln ( x )}{x ^{4}} d x

簡素化

= (- 2) \cdot \int \frac{x ln ( x )}{x ^{4}} d x

共通因数を約分する:

x

= (- 2) \cdot \int \frac{ln ( x )}{x ^{3}} d x

部分積分を適用する

= (- 2) (- \frac{ln ( x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x)

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

= (- 2) (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}})

簡素化

(- 2) (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}) : \frac{ln ( x )}{x ^{2}} + \frac{1}{2 x ^{2}}

= \frac{ln ( x )}{x ^{2}} + \frac{1}{2 x ^{2}}

定数を解答に追加する

= \frac{ln ( x )}{x ^{2}} + \frac{1}{2 x ^{2}} + C

グラフ

人気の例

(\partial)/(\partial x)(k(1+ae^{-b(x,w,t)x})(1+cos(wt)))

\frac{\partial}{\partial x} (k (1 + a e^{- b (x, w, t) x}) (1 + cos (wt)))

derivative of (7x+4^2)

\frac{d}{d x} ((7 x + 4)^{2})

integral of 7/(xsqrt(4-49ln^2(x)))

\int \frac{7}{x 4 - 49 ln ^{2} ( x )} d x

integral of 3x(sqrt(5-x))

\int 3 x (5 - x) d x

y^{''}+9y=tan(3x)

y^{^{''}} + 9 y = tan (3 x)