What is the solution for f^'(x)=sqrt(x)(6+5x) ?

The solution for f^'(x)=sqrt(x)(6+5x) is f(x)=4x^{3/2}+2x^{5/2}+c_{1}

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f^'(x)=sqrt(x)(6+5x)

f^{^{'}} (x) = x (6 + 5 x)

f (x) = 4 x^{\frac{3}{2}} + 2 x^{\frac{5}{2}} + c_{1}

Solution steps

f^{'} (x) = x (6 + 5 x)

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

then

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

f (x) = \int x (6 + 5 x) d x

\int x (6 + 5 x) d x = 4 x^{\frac{3}{2}} + 2 x^{\frac{5}{2}} + c_{1}

f (x) = 4 x^{\frac{3}{2}} + 2 x^{\frac{5}{2}} + c_{1}

f (x) = \frac{1}{10 x}, at x = 9

\int x^{6} + \frac{1}{1 - 4 x ^{2}} d x

e^{- 4 t}

(i)^{^{'}}

\frac{d}{d x} (1 + tan^{2} (x))

What is the solution for f^'(x)=sqrt(x)(6+5x) ?
The solution for f^'(x)=sqrt(x)(6+5x) is f(x)=4x^{3/2}+2x^{5/2}+c_{1}