What is the solution for (dy)/(dx)=5^xln(5)+1/(x^2+1) ?

The solution for (dy)/(dx)=5^xln(5)+1/(x^2+1) is y=5^x+arctan(x)+c_{1}

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(dy)/(dx)=5^xln(5)+1/(x^2+1)

\frac{d y}{d x} = 5^{x} ln (5) + \frac{1}{x ^{2} + 1}

y = 5^{x} + arctan (x) + c_{1}

Solution steps

\frac{d y}{d x} = 5^{x} ln (5) + \frac{1}{x ^{2} + 1}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 5^{x} ln (5) + \frac{1}{x ^{2} + 1}

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

then

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

y = \int 5^{x} ln (5) + \frac{1}{x ^{2} + 1} d x

\int 5^{x} ln (5) + \frac{1}{x ^{2} + 1} d x = 5^{x} + arctan (x) + c_{1}

y = 5^{x} + arctan (x) + c_{1}

\frac{d}{d x} (sin (23 x))

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

\int csc^{15} (x) d x

\int_{1}^{5} \frac{4}{x ^{2} + 2 x + 1} d x

\int \frac{sin ( x )}{cos ^{3} ( x )} d x

What is the solution for (dy)/(dx)=5^xln(5)+1/(x^2+1) ?
The solution for (dy)/(dx)=5^xln(5)+1/(x^2+1) is y=5^x+arctan(x)+c_{1}