integral of (8sqrt(x^3)+3\sqrt[3]{x^2})

Lösung

\int (8 x^{3} + 3 3 x^{2}) d x

\frac{16}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} + C

Schritte zur Lösung

\int 8 x^{3} + 3 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 8 x^{3} d x + \int 3 3 x^{2} d x

\int 8 x^{3} d x = \frac{16}{5} x^{\frac{5}{2}}

\int 3 3 x^{2} d x = \frac{9}{5} x^{\frac{5}{3}}

= \frac{16}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{16}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} + C

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{14}} d x

\int \frac{e ^{3 x}}{( e ^{3 x} + 2 ) ^{- 4}} d x

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

\int \frac{2 - 4 x}{( x + 2 ) ( x - 3 )} d x

\int - 2 x^{2} + 2 x + 4 d x