What is the solution for (dy)/(dx)=5cos^3(3x+6) ?

The solution for (dy)/(dx)=5cos^3(3x+6) is y= 5/3 (sin(3x+6)-1/3 sin^3(3x+6))+c_{1}

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(dy)/(dx)=5cos^3(3x+6)

\frac{d y}{d x} = 5 cos^{3} (3 x + 6)

y = \frac{5}{3} (sin (3 x + 6) - \frac{1}{3} sin^{3} (3 x + 6)) + c_{1}

Solution steps

\frac{d y}{d x} = 5 cos^{3} (3 x + 6)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 5 cos^{3} (3 x + 6)

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

then

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

y = \int 5 cos^{3} (3 x + 6) d x

\int 5 cos^{3} (3 x + 6) d x = \frac{5}{3} (sin (3 x + 6) - \frac{1}{3} sin^{3} (3 x + 6)) + c_{1}

y = \frac{5}{3} (sin (3 x + 6) - \frac{1}{3} sin^{3} (3 x + 6)) + c_{1}

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What is the solution for (dy)/(dx)=5cos^3(3x+6) ?
The solution for (dy)/(dx)=5cos^3(3x+6) is y= 5/3 (sin(3x+6)-1/3 sin^3(3x+6))+c_{1}