de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (3-1/x)^{-2}(1/(x^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

= - \frac{x}{( 3 x - 1 ) ^{2}} + \frac{1}{3 ( 3 x - 1 ) ^{2}} + C

Graph

Beliebte Beispiele

integral of (x^3)/((5-x^4)^5)

\int \frac{x ^{3}}{( 5 - x ^{4} ) ^{5}} d x

tangent y=4(x-1/x)^3,\at x=2

t an g e n t y = 4 (x - \frac{1}{x})^{3}, at x = 2

integral of 1/((x-1)sqrt(4x^2-8x+3))

\int \frac{1}{( x - 1 ) 4 x ^{2} - 8 x + 3} d x

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

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

y^{''}-y=0,y(0)=0,y^'(0)=1

y^{^{''}} - y = 0, y (0) = 0, y^{^{'}} (0) = 1