What is the solution for f^'(x)=5e^x+3x^2-2x ?

The solution for f^'(x)=5e^x+3x^2-2x is f(x)=5e^x+x^3-x^2+c_{1}

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f^'(x)=5e^x+3x^2-2x

f^{^{'}} (x) = 5 e^{x} + 3 x^{2} - 2 x

f (x) = 5 e^{x} + x^{3} - x^{2} + c_{1}

Solution steps

f^{'} (x) = 5 e^{x} + 3 x^{2} - 2 x

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

then

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

f (x) = \int 5 e^{x} + 3 x^{2} - 2 x d x

\int 5 e^{x} + 3 x^{2} - 2 x d x = 5 e^{x} + x^{3} - x^{2} + c_{1}

f (x) = 5 e^{x} + x^{3} - x^{2} + c_{1}

\frac{\partial}{\partial x} (x^{2} + x y^{2})

\int \frac{1}{6 x ( 5 + x )} d x

6 y^{^{''}} + 31 y = 0

x \to 4 lim (\frac{x ^{3} - 6}{x - 4})

x \to - 3 lim (\frac{x}{x - 3})

What is the solution for f^'(x)=5e^x+3x^2-2x ?
The solution for f^'(x)=5e^x+3x^2-2x is f(x)=5e^x+x^3-x^2+c_{1}