(dy)/(dx)=16xsec^2(4x)

解

\frac{d y}{d x} = 16 x sec^{2} (4 x)

y = 8 x^{2} sec^{2} (4 x) - 8 x^{2} tan^{2} (4 x) + 4 x tan (4 x) + ln (cos (4 x)) - 8 x^{2} + c_{1}

解答ステップ

\frac{d y}{d x} = 16 x sec^{2} (4 x)

代用

\frac{d y}{d x}

と

y^{'} (x)

y^{^{'}} (x) = 16 x sec^{2} (4 x)

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

であれば

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

y = \int 16 x sec^{2} (4 x) d x

\int 16 x sec^{2} (4 x) d x = 8 x^{2} sec^{2} (4 x) - 8 x^{2} tan^{2} (4 x) + 4 x tan (4 x) + ln (cos (4 x)) - 8 x^{2} + c_{1}

y = 8 x^{2} sec^{2} (4 x) - 8 x^{2} tan^{2} (4 x) + 4 x tan (4 x) + ln (cos (4 x)) - 8 x^{2} + c_{1}