de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of ((x-1))/((x-1)^2+1)

Lösung

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

Lösung

\frac{1}{2} ln x^{2} - 2 x + 2 + C

Schritte zur Lösung

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

Multipliziere aus

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

Wende die Summenregel an:

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

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

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

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

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

Vereinfache

= \frac{1}{2} ln x^{2} - 2 x + 2

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

inverselaplace 1/(s^{3/2)}

in v erse l a pl a ce \frac{1}{s ^{\frac{3}{2}}}

6y^{''}+31y=0,y(0)=6,y^'(0)=2

6 y^{^{''}} + 31 y = 0, y (0) = 6, y^{^{'}} (0) = 2

derivative of 1/(y^2+x)

\frac{d}{d x} (\frac{1}{y ^{2} + x})

tangent y= 1/(x^2),(3, 1/9)

t an g e n t y = \frac{1}{x ^{2}}, (3, \frac{1}{9})

(dy)/(dx)-9/x y=(y^3)/(x^{13)}

\frac{d y}{d x} - \frac{9}{x} y = \frac{y ^{3}}{x ^{13}}