(dy)/(dx)=x^4(32-x^5)^5

Lösung

\frac{d y}{d x} = x^{4} (32 - x^{5})^{5}

y = \frac{33554432 x ^{5}}{5} - 524288 x^{10} + \frac{65536 x ^{15}}{3} - 512 x^{20} + \frac{32 x ^{25}}{5} - \frac{x ^{30}}{30} + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = x^{4} (32 - x^{5})^{5}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = x^{4} (32 - x^{5})^{5}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

y = \int x^{4} (32 - x^{5})^{5} d x

\int x^{4} (32 - x^{5})^{5} d x = \frac{33554432 x ^{5}}{5} - 524288 x^{10} + \frac{65536 x ^{15}}{3} - 512 x^{20} + \frac{32 x ^{25}}{5} - \frac{x ^{30}}{30} + c_{1}

y = \frac{33554432 x ^{5}}{5} - 524288 x^{10} + \frac{65536 x ^{15}}{3} - 512 x^{20} + \frac{32 x ^{25}}{5} - \frac{x ^{30}}{30} + c_{1}

s l o p e in t erce pt (- 1.6) (1.5)

t a y l or ln (x), x = 1

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

d er i v a t i v e y = ln (x^{2} - 4)

x \to 2 lim (3 - x^{\frac{1}{x ^{2}}})