integral of (x^5-3125)/(x-5)

Lösung

\int \frac{x ^{5} - 3125}{x - 5} d x

\frac{x ^{5}}{5} + \frac{5 x ^{4}}{4} + \frac{25 x ^{3}}{3} + \frac{125 x ^{2}}{2} + 625 x + C

Schritte zur Lösung

\int \frac{x ^{5} - 3125}{x - 5} d x

Vereinfache

\frac{x ^{5} - 3125}{x - 5} : x^{4} + 5 x^{3} + 25 x^{2} + 125 x + 625

= \int x^{4} + 5 x^{3} + 25 x^{2} + 125 x + 625 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^{4} d x + \int 5 x^{3} d x + \int 25 x^{2} d x + \int 125 x d x + \int 625 d x

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

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 25 x^{2} d x = \frac{25 x ^{3}}{3}

\int 125 x d x = \frac{125 x ^{2}}{2}

\int 625 d x = 625 x

= \frac{x ^{5}}{5} + \frac{5 x ^{4}}{4} + \frac{25 x ^{3}}{3} + \frac{125 x ^{2}}{2} + 625 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} + \frac{5 x ^{4}}{4} + \frac{25 x ^{3}}{3} + \frac{125 x ^{2}}{2} + 625 x + C

t an g e n t f (x) = 3 x^{2} + 12 x - 36

\int - \frac{10}{x ^{2} + 16} d x

- y^{^{''}} + 36 y = 0

\frac{d}{d x} (x^{\frac{7}{2}})

d er i v a t i v e 6 y