integral of x^{-1}+x^{1/3}+5/3

Lösung

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

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

Schritte zur Lösung

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

\int x^{- 1} d x = ln ∣ x ∣

\int x^{\frac{1}{3}} d x = \frac{3}{4} x^{\frac{4}{3}}

\int \frac{5}{3} d x = \frac{5}{3} x

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} (\frac{1}{2} x^{- \frac{1}{2}})

\int 50 - 6.3 e^{0.9 x} d x

\int (3 x + 2)^{5} d x

d er i v a t i v e f (x) = \frac{x}{x ^{2} + 1}

\frac{\partial}{\partial x} (8 x (x^{2} + y^{2})^{- \frac{1}{2}})