What is the solution for f^'(x)=x*15^x ?

The solution for f^'(x)=x*15^x is f(x)=(15^xx)/(ln(15))-(15^x)/(ln^2(15))+c_{1}

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

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}

Solution steps

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

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

then

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}

\frac{x}{2 x + 3}

\int_{1}^{16} \frac{6}{x} d x

\int_{2}^{5} \frac{1}{2 - 5 t} d t

9 y^{^{''}} - 6 y^{^{'}} + 4 y = 0

\frac{d}{d x} ((1 - x) e^{- x})

What is the solution for f^'(x)=x*15^x ?
The solution for f^'(x)=x*15^x is f(x)=(15^xx)/(ln(15))-(15^x)/(ln^2(15))+c_{1}