integral of 4x^3-5x+5+1/x+3/(x^2)

Lösung

\int 4 x^{3} - 5 x + 5 + \frac{1}{x} + \frac{3}{x ^{2}} d x

x^{4} - \frac{5 x ^{2}}{2} + 5 x + ln ∣ x ∣ - \frac{3}{x} + C

Schritte zur Lösung

\int 4 x^{3} - 5 x + 5 + \frac{1}{x} + \frac{3}{x ^{2}} 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 x^{3} d x - \int 5 x d x + \int 5 d x + \int \frac{1}{x} d x + \int \frac{3}{x ^{2}} d x

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

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

\int 5 d x = 5 x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= x^{4} - \frac{5 x ^{2}}{2} + 5 x + ln ∣ x ∣ - \frac{3}{x}

Füge eine Konstante zur Lösung hinzu

= x^{4} - \frac{5 x ^{2}}{2} + 5 x + ln ∣ x ∣ - \frac{3}{x} + C

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