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

解

\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}

解答ステップ

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

代用

\frac{d y}{d x}

と

y^{'} (x)

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

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

であれば

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}