integral of (10)/x+2/(x^2)+7/(x^3)

Lösung

\int \frac{10}{x} + \frac{2}{x ^{2}} + \frac{7}{x ^{3}} d x

10 ln ∣ x ∣ - \frac{2}{x} - \frac{7}{2 x ^{2}} + C

Schritte zur Lösung

\int \frac{10}{x} + \frac{2}{x ^{2}} + \frac{7}{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 \frac{10}{x} d x + \int \frac{2}{x ^{2}} d x + \int \frac{7}{x ^{3}} d x

\int \frac{10}{x} d x = 10 ln ∣ x ∣

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

\int \frac{7}{x ^{3}} d x = - \frac{7}{2 x ^{2}}

= 10 ln ∣ x ∣ - \frac{2}{x} - \frac{7}{2 x ^{2}}

Füge eine Konstante zur Lösung hinzu

= 10 ln ∣ x ∣ - \frac{2}{x} - \frac{7}{2 x ^{2}} + C

\int 1 + \frac{1}{4 x} d x

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

x \to 4 lim (\frac{6 x - 1}{2 x - 9})

\int - 2.1 x d x

\int_{0}^{4} (4 x + 7) d x