f^'(x)=x*15^x

解

f^{^{'}} (x) = x \cdot 1 5^{x}

f (x) = \frac{1 5 ^{x} x}{ln ( 15 )} - \frac{1 5 ^{x}}{ln ^{2} ( 15 )} + c_{1}

解答ステップ

f^{'} (x) = x \cdot 1 5^{x}

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

であれば

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

f (x) = \int x \cdot 1 5^{x} d x

\int x \cdot 1 5^{x} d x = \frac{1 5 ^{x} x}{ln ( 15 )} - \frac{1 5 ^{x}}{ln ^{2} ( 15 )} + c_{1}

f (x) = \frac{1 5 ^{x} x}{ln ( 15 )} - \frac{1 5 ^{x}}{ln ^{2} ( 15 )} + c_{1}