integral of x(x+5)^4

Lösung

\int x (x + 5)^{4} d x

\frac{x ^{6}}{6} + 4 x^{5} + \frac{75 x ^{4}}{2} + \frac{500 x ^{3}}{3} + \frac{625 x ^{2}}{2} + C

Schritte zur Lösung

\int x (x + 5)^{4} d x

Multipliziere aus

x (x + 5)^{4} : x^{5} + 20 x^{4} + 150 x^{3} + 500 x^{2} + 625 x

= \int x^{5} + 20 x^{4} + 150 x^{3} + 500 x^{2} + 625 x 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 20 x^{4} d x + \int 150 x^{3} d x + \int 500 x^{2} d x + \int 625 x d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 20 x^{4} d x = 4 x^{5}

\int 150 x^{3} d x = \frac{75 x ^{4}}{2}

\int 500 x^{2} d x = \frac{500 x ^{3}}{3}

\int 625 x d x = \frac{625 x ^{2}}{2}

= \frac{x ^{6}}{6} + 4 x^{5} + \frac{75 x ^{4}}{2} + \frac{500 x ^{3}}{3} + \frac{625 x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{6} + 4 x^{5} + \frac{75 x ^{4}}{2} + \frac{500 x ^{3}}{3} + \frac{625 x ^{2}}{2} + C

\int cos^{(3)} (5 x) sin^{- 2} (5 x) d x

\frac{\partial}{\partial x} (e^{x^{5}})

\frac{\partial}{\partial x} (\frac{x}{( 1 - x ) ^{2}})

\frac{\partial}{\partial y} (\frac{1}{x ^{3} - y ^{2}})

t an g e n t f (x) = x^{2} + 3, at x = 1