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

Lösung

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

- \frac{1}{4 x ^{4}} + \frac{2}{3} x^{\frac{3}{2}} + C

Schritte zur Lösung

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

\int x^{- 5} d x = - \frac{1}{4 x ^{4}}

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

= - \frac{1}{4 x ^{4}} + \frac{2}{3} x^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4 x ^{4}} + \frac{2}{3} x^{\frac{3}{2}} + C

\frac{d}{d x} ((- x^{2} + 25)^{2})

\int \frac{7}{x ^{3} - 125} d x

\frac{\partial}{\partial y} (sin^{2} (x - 3 y))

\frac{d}{d x} (s cos (x))

n = 2 \sum \infty \frac{1}{n ^{4}}