integral of (x+1)/((x-1)^3)

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{tan ( x )}{1} d x

y^{^{'}} = t - 2 y

t an g e n t f (x) = x^{2} - 7 x + 12, at x = 2

d er i v a t i v e y = 4 - 4 + x

\frac{d}{d r ( t )} (\frac{s - r ( t )}{t})