integral of (4x^5+x^4-3x^2)/(x^2)

Lösung

\int \frac{4 x ^{5} + x ^{4} - 3 x ^{2}}{x ^{2}} d x

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

Schritte zur Lösung

\int \frac{4 x ^{5} + x ^{4} - 3 x ^{2}}{x ^{2}} d x

Multipliziere aus

\frac{4 x ^{5} + x ^{4} - 3 x ^{2}}{x ^{2}} : \frac{4 x ^{5}}{x ^{2}} + \frac{x ^{4}}{x ^{2}} - \frac{3 x ^{2}}{x ^{2}}

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{4 x ^{5}}{x ^{2}} d x + \int \frac{x ^{4}}{x ^{2}} d x - \int \frac{3 x ^{2}}{x ^{2}} d x

\int \frac{4 x ^{5}}{x ^{2}} d x = x^{4}

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int e^{- x - e^{- x}} d x

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

\int \frac{sinh ( x )}{1 + sinh ^{2} ( x )} d x

\int x^{\frac{1}{n}} d x

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