Please solve this question . I am getting 2 instead of 2/3 here.

Dear Student,

Please find the below required solution.

$$\begin{gathered} I think the question is integrate the foloowing. \\ Let I=\int (3\cos e{c}^{2}x+2\sin 3x)dx \\ = 3\int \cos e{c}^{2}xdx+2\int \sin 3xdx \\ = 3(-cotx)+2\left(-\frac{\cos 3x}{3}\right)+c [ Since \int \cos e{c}^{2}xdx=-cotx, \int \sin axdx = -(\cos ax/a) ] \\ = -3cotx-\frac{2}{3}\cos 3x+c \end{gathered}$$

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