integral of (4x^3+3x-8)/(x^3)

Lösung

\int \frac{4 x ^{3} + 3 x - 8}{x ^{3}} d x

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

Schritte zur Lösung

\int \frac{4 x ^{3} + 3 x - 8}{x ^{3}} d x

Multipliziere aus

\frac{4 x ^{3} + 3 x - 8}{x ^{3}} : 4 + \frac{3}{x ^{2}} - \frac{8}{x ^{3}}

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

\int 4 d x = 4 x

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int (sin (x)) (sec^{2} (x)) d x

\int x^{2} (x^{3} + 4) d x

\int \frac{2 x ^{2} + 2 x - 7}{x ^{2} - 4} d x

\int 7 x^{\frac{2}{5}} - 18 x^{\frac{4}{5}} d x

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