Evaluate
\frac{t\left(\sin(u)+\cos(u)-1\right)}{\sin(2u)}+С
\nexists n_{1}\in \mathrm{Z}\text{ : }u=\frac{\pi n_{1}}{2}
Differentiate w.r.t. u
\frac{2t\left(\left(\sin(u)\right)^{3}-\left(\cos(u)\right)^{3}+\cos(2u)\right)}{\left(\sin(2u)\right)^{2}}
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\frac{\sin(u)+\cos(u)-1}{\frac{1}{2}\times 2\sin(2u)}t
Find the integral of \frac{\sin(u)+\cos(u)-1}{\frac{1}{2}\times 2\sin(2u)} using the table of common integrals rule \int a\mathrm{d}t=at.
\frac{\left(\sin(u)+\cos(u)-1\right)t}{\frac{1}{2}\times 2\sin(2u)}
Simplify.
\begin{matrix}\frac{\left(\sin(u)+\cos(u)-1\right)t}{\frac{1}{2}\times 2\sin(2u)}+С_{3},&\end{matrix}
If F\left(t\right) is an antiderivative of f\left(t\right), then the set of all antiderivatives of f\left(t\right) is given by F\left(t\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
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