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 (sin(1/x)-1/x+1) 1/(x^2)

解

\int (sin (\frac{1}{x}) - \frac{1}{x} + 1) \frac{1}{x ^{2}} d x

解

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

解答ステップ

\int (sin (\frac{1}{x}) - \frac{1}{x} + 1) \frac{1}{x ^{2}} d x

簡素化

(sin (\frac{1}{x}) - \frac{1}{x} + 1) \frac{1}{x ^{2}} : \frac{x sin ( \frac{1}{x} ) - 1 + x}{x ^{3}}

= \int \frac{x sin ( \frac{1}{x} ) - 1 + x}{x ^{3}} d x

拡張

\frac{x sin ( \frac{1}{x} ) - 1 + x}{x ^{3}} : \frac{sin ( \frac{1}{x} )}{x ^{2}} - \frac{1}{x ^{3}} + \frac{1}{x ^{2}}

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

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{sin ( \frac{1}{x} )}{x ^{2}} d x = cos (\frac{1}{x})

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

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

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

簡素化

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

定数を解答に追加する

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

グラフ

人気の例

integral of sin(1-5x)

\int sin (1 - 5 x) d x

integral of (x/(sqrt(x^2+9)))

\int (\frac{x}{x ^{2} + 9}) d x

integral of t^2e^{-15t}

\int t^{2} e^{- 15 t} d t

integral of 1/2 x^{-1/2}e^{sqrt(x)}

\int \frac{1}{2} x^{- \frac{1}{2}} e^{x} d x

integral of 1/(sqrt(4s))

\int \frac{1}{4 s} d s