Evaluate
\frac{\ln(|\sin(3x)|)}{3}+С
Differentiate w.r.t. x
\cot(3x)
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\int \frac{\left(\sin(3x)\right)^{2}\cos(3x)+\left(\cos(3x)\right)^{3}}{\sin(3x)}\mathrm{d}x
Use the distributive property to multiply \left(\sin(3x)\right)^{2}+\left(\cos(3x)\right)^{2} by \cos(3x).
\frac{\ln(|\sin(3x)|)}{3}
Simplify.
\frac{\ln(|\sin(3x)|)}{3}+С
If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
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