What is the solution for f^'(x)=5(1+e^x)^4e^x ?

The solution for f^'(x)=5(1+e^x)^4e^x is f(x)=(1+e^x)^5+c_{1}

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f^'(x)=5(1+e^x)^4e^x

f^{^{'}} (x) = 5 (1 + e^{x})^{4} e^{x}

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

Solution steps

f^{'} (x) = 5 (1 + e^{x})^{4} e^{x}

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

then

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

f (x) = \int 5 (1 + e^{x})^{4} e^{x} d x

\int 5 (1 + e^{x})^{4} e^{x} d x = (1 + e^{x})^{5} + c_{1}

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

h (w) = \frac{5 w ^{3} - w}{w}

\frac{d}{d x} ((x^{2} - 3)^{4})

\frac{d}{d x} ((a + \frac{b}{x ^{2}})^{3})

x y^{3}

\frac{4 2}{3} x^{\frac{3}{2}} - 1

What is the solution for f^'(x)=5(1+e^x)^4e^x ?
The solution for f^'(x)=5(1+e^x)^4e^x is f(x)=(1+e^x)^5+c_{1}