integral of x^{5/2}-x^{1/2}

Lösung

\int x^{\frac{5}{2}} - x^{\frac{1}{2}} d x

\frac{2}{7} x^{\frac{7}{2}} - \frac{2}{3} x^{\frac{3}{2}} + C

Schritte zur Lösung

\int x^{\frac{5}{2}} - x^{\frac{1}{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 x^{\frac{5}{2}} d x - \int x^{\frac{1}{2}} d x

\int x^{\frac{5}{2}} d x = \frac{2}{7} x^{\frac{7}{2}}

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

= \frac{2}{7} x^{\frac{7}{2}} - \frac{2}{3} x^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{7} x^{\frac{7}{2}} - \frac{2}{3} x^{\frac{3}{2}} + C

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

\int 16 e^{- 4 x} d x

\int 3 \cdot cos (x) + 3 x + 2 d x

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

\int \frac{x ^{2} - 9}{2 x} d x