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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{4} + x - 3}{x ^{3}} : x + \frac{1}{x ^{2}} - \frac{3}{x ^{3}}

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

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

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of x^2sqrt(12+x^3)

\int x^{2} 12 + x^{3} d x

integral of (3-x)/2

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

integral of (2x-1)/((x-2)(x-3)(x+1))

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

integral of (a^2-2x^2)^4*(20x)

\int (a^{2} - 2 x^{2})^{4} \cdot (20 x) d x

integral of (2x^3)/(1+x^2)

\int \frac{2 x ^{3}}{1 + x ^{2}} d x