What is the solution for (df)/(dθ)=sin(θ)+csc(θ) ?

The solution for (df)/(dθ)=sin(θ)+csc(θ) is f(θ)=-cos(θ)+ln(tan(θ/2))+c_{1}

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(df)/(dθ)=sin(θ)+csc(θ)

\frac{df}{d θ} = sin (θ) + csc (θ)

f (θ) = - cos (θ) + ln (tan (\frac{θ}{2})) + c_{1}

Solution steps

\frac{df}{d θ} = sin (θ) + csc (θ)

Substitute

\frac{df}{d θ}

with

f^{'} (θ)

f^{^{'}} (θ) = sin (θ) + csc (θ)

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

then

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

f (θ) = \int sin (θ) + csc (θ) d θ

\int sin (θ) + csc (θ) d θ = - cos (θ) + ln (tan (\frac{θ}{2})) + c_{1}

f (θ) = - cos (θ) + ln (tan (\frac{θ}{2})) + c_{1}

What is the solution for (df)/(dθ)=sin(θ)+csc(θ) ?
The solution for (df)/(dθ)=sin(θ)+csc(θ) is f(θ)=-cos(θ)+ln(tan(θ/2))+c_{1}