What is the solution for (dy)/(dx)=2^xln(2)+2/(x^2+1) ?

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

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(dy)/(dx)=2^xln(2)+2/(x^2+1)

\frac{d y}{d x} = 2^{x} ln (2) + \frac{2}{x ^{2} + 1}

y = 2^{x} + 2 arctan (x) + c_{1}

Solution steps

\frac{d y}{d x} = 2^{x} ln (2) + \frac{2}{x ^{2} + 1}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 2^{x} ln (2) + \frac{2}{x ^{2} + 1}

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

then

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

y = \int 2^{x} ln (2) + \frac{2}{x ^{2} + 1} d x

\int 2^{x} ln (2) + \frac{2}{x ^{2} + 1} d x = 2^{x} + 2 arctan (x) + c_{1}

y = 2^{x} + 2 arctan (x) + c_{1}

a re a x^{2} + 4, - x^{2} - 1, - 2, 3

\frac{\partial}{\partial x} (cos (- t + y + e^{x}))

\frac{d}{d x} (ln (cos (ln (x))))

\frac{d y}{d t} = 3 t e^{- y}

d er i v a t i v e y = x arcsin (2 x)

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