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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

partialfraction (-2x^2)/(x^2-1)

p a r t ia l f r a c t i o n \frac{- 2 x ^{2}}{x ^{2} - 1}

derivative of-3x^2+24x+10

\frac{d}{d x} (- 3 x^{2} + 24 x + 10)

(\partial)/(\partial y)(e^xsec^2(y))

\frac{\partial}{\partial y} (e^{x} sec^{2} (y))

tangent f(x)=x^2-8,(4,8)

t an g e n t f (x) = x^{2} - 8, (4, 8)

tangent y=9x-6sqrt(x),(1,3)

t an g e n t y = 9 x - 6 x, (1, 3)