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Beliebt Rechnen >

integral of ((6x-8)/((x-3)^3))

Lösung

\int (\frac{6 x - 8}{( x - 3 ) ^{3}}) d x

Lösung

- \frac{6}{x - 3} - \frac{5}{( x - 3 ) ^{2}} + C

Schritte zur Lösung

\int \frac{6 x - 8}{( x - 3 ) ^{3}} d x

Multipliziere aus

\frac{6 x - 8}{( x - 3 ) ^{3}} : \frac{6 x}{( x - 3 ) ^{3}} - \frac{8}{( x - 3 ) ^{3}}

= \int \frac{6 x}{( x - 3 ) ^{3}} - \frac{8}{( x - 3 ) ^{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{6 x}{( x - 3 ) ^{3}} d x - \int \frac{8}{( x - 3 ) ^{3}} d x

\int \frac{6 x}{( x - 3 ) ^{3}} d x = 6 (- \frac{1}{x - 3} - \frac{3}{2 ( x - 3 ) ^{2}})

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

= 6 (- \frac{1}{x - 3} - \frac{3}{2 ( x - 3 ) ^{2}}) - (- \frac{4}{( x - 3 ) ^{2}})

Vereinfache

6 (- \frac{1}{x - 3} - \frac{3}{2 ( x - 3 ) ^{2}}) - (- \frac{4}{( x - 3 ) ^{2}}) : - \frac{6}{x - 3} - \frac{5}{( x - 3 ) ^{2}}

= - \frac{6}{x - 3} - \frac{5}{( x - 3 ) ^{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{6}{x - 3} - \frac{5}{( x - 3 ) ^{2}} + C

Graph

Beliebte Beispiele

integral of x/(x^3+8)

\int \frac{x}{x ^{3} + 8} d x

integral of (cos(pi/(x^{23)}))/(x^{24)}

\int \frac{cos ( \frac{π}{x ^{23}} )}{x ^{24}} d x

integral of (3x^4-5x^3-x-6)

\int (3 x^{4} - 5 x^{3} - x - 6) d x

integral of x(e^{x^2}-3)^2

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

integral of (cos(pi/(x^{29)}))/(x^{30)}

\int \frac{cos ( \frac{π}{x ^{29}} )}{x ^{30}} d x