(df)/(dx)=tan^3(x)-sec^3(x)

解

\frac{df}{d x} = tan^{3} (x) - sec^{3} (x)

f (x) = - ln (sec (x)) + \frac{1}{2} sec^{2} (x) - \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln (tan (x) + sec (x)) + c_{1}

解答ステップ

\frac{df}{d x} = tan^{3} (x) - sec^{3} (x)

代用

\frac{df}{d x}

と

f^{'} (x)

f^{^{'}} (x) = tan^{3} (x) - sec^{3} (x)

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

であれば

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

f (x) = \int tan^{3} (x) - sec^{3} (x) d x

\int tan^{3} (x) - sec^{3} (x) d x = - ln (sec (x)) + \frac{1}{2} sec^{2} (x) - \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln (tan (x) + sec (x)) + c_{1}

f (x) = - ln (sec (x)) + \frac{1}{2} sec^{2} (x) - \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln (tan (x) + sec (x)) + c_{1}