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Beliebt Rechnen >

integral of (3x^3-4x-2)/(x^3)

Lösung

\int \frac{3 x ^{3} - 4 x - 2}{x ^{3}} d x

Lösung

3 x + \frac{4}{x} + \frac{1}{x ^{2}} + C

Schritte zur Lösung

\int \frac{3 x ^{3} - 4 x - 2}{x ^{3}} d x

Multipliziere aus

\frac{3 x ^{3} - 4 x - 2}{x ^{3}} : 3 - \frac{4}{x ^{2}} - \frac{2}{x ^{3}}

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

\int 3 d x = 3 x

\int \frac{4}{x ^{2}} d x = - \frac{4}{x}

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

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

Vereinfache

= 3 x + \frac{4}{x} + \frac{1}{x ^{2}}

Füge eine Konstante zur Lösung hinzu

= 3 x + \frac{4}{x} + \frac{1}{x ^{2}} + C

Graph

Beliebte Beispiele

inverselaplace ((x+5))/((x^2+5x+6))

in v erse l a pl a ce \frac{( x + 5 )}{( x ^{2} + 5 x + 6 )}

y^{''}-2y^'-3y=-9te-t

y^{^{''}} - 2 y^{^{'}} - 3 y = - 9 t e - t

integral of 2x+4xln(8x)

\int 2 x + 4 x ln (8 x) d x

integral from-2 to 2 of 3

\int_{- 2}^{2} 3

tangent f(x)=4-3x^2,(5,-71)

t an g e n t f (x) = 4 - 3 x^{2}, (5, - 71)