integral of (\sqrt[3]{x}-1/(sqrt(x)))

Lösung

\int (3 x - \frac{1}{x}) d x

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

Schritte zur Lösung

\int 3 x - \frac{1}{x} 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 3 x d x - \int \frac{1}{x} d x

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

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

= \frac{3}{4} x^{\frac{4}{3}} - 2 x

Füge eine Konstante zur Lösung hinzu

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

\int 3 e^{5 x - 2} cos (7 - 4 x) d x

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

\int \frac{1}{x + a ^{2} - x ^{2}} d x

\int \frac{x ^{2}}{( 1 - x ) ^{2021}} d x

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