integral of 3sqrt(x)-\sqrt[3]{x^5}

Lösung

\int 3 x - 3 x^{5} d x

2 x^{\frac{3}{2}} - \frac{3}{8} x^{\frac{8}{3}} + C

Schritte zur Lösung

\int 3 x - 3 x^{5} 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 3 x^{5} d x

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

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

= 2 x^{\frac{3}{2}} - \frac{3}{8} x^{\frac{8}{3}}

Füge eine Konstante zur Lösung hinzu

= 2 x^{\frac{3}{2}} - \frac{3}{8} x^{\frac{8}{3}} + C

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

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

\int \frac{( 6 + sin ( x ) )}{cos ( x )} d x

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

\int \frac{4}{x ^{4} x ^{2} - 8} d x