integral of 6^3+3/x+1/(x^2)

Lösung

\int 6^{3} + \frac{3}{x} + \frac{1}{x ^{2}} d x

216 x + 3 ln ∣ x ∣ - \frac{1}{x} + C

Schritte zur Lösung

\int 6^{3} + \frac{3}{x} + \frac{1}{x ^{2}} d x

Vereinfache

= \int 216 + \frac{3}{x} + \frac{1}{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 216 d x + \int \frac{3}{x} d x + \int \frac{1}{x ^{2}} d x

\int 216 d x = 216 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 216 x + 3 ln ∣ x ∣ - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= 216 x + 3 ln ∣ x ∣ - \frac{1}{x} + C

in v erse l a pl a ce {\frac{1}{S ^{2} + 3 S}}

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

\frac{\partial}{\partial z} (2 x z)

\int \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

\frac{\partial}{\partial x} (3 x^{2} + 2 y^{2})