What is the solution for (dy)/(dx)=cos^2(x) ?

The solution for (dy)/(dx)=cos^2(x) is y= 1/2 (x+1/2 sin(2x))+c_{1}

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(dy)/(dx)=cos^2(x)

\frac{d y}{d x} = cos^{2} (x)

y = \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + c_{1}

Solution steps

\frac{d y}{d x} = cos^{2} (x)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = cos^{2} (x)

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

then

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

y = \int cos^{2} (x) d x

\int cos^{2} (x) d x = \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + c_{1}

y = \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + c_{1}

\frac{d}{d x} (2 x^{2} sin (x) tan (x))

\int \frac{8000 ln ( x + 40 )}{( x + 40 ) ^{2}} d x

\int_{0}^{2} 10 d x

\int x^{2} - 4 - x^{2} d x

\frac{d y}{d x} = \frac{3 x}{y}

What is the solution for (dy)/(dx)=cos^2(x) ?
The solution for (dy)/(dx)=cos^2(x) is y= 1/2 (x+1/2 sin(2x))+c_{1}