int (3 csc^2 x + 2 sin 3x) , dx = | vedclass

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Question

(B) We need to evaluate the integral $\int (3 \csc^2 x + 2 \sin 3x) \, dx$. Using the linearity property of integration,we can write this as $\int 3 \

Vedclass · Accepted Answer

$- (3 \cot x + \frac{2}{3} \cos 3x) + c$

Vedclass · Answer

(B) We need to evaluate the integral $\int (3 \csc^2 x + 2 \sin 3x) \, dx$. Using the linearity property of integration,we can write this as $\int 3 \csc^2 x \, dx + \int 2 \sin 3x \, dx$. The integral of $\csc^2 x$ is $-\cot x$ and the integral of $\sin(ax)$ is $-\frac{1}{a} \cos(ax)$. Thus,$\int 3 \csc^2 x \, dx = -3 \cot x$ and $\int 2 \sin 3x \, dx = 2 \left( -\frac{1}{3} \cos 3x \right) = -\frac{2}{3} \cos 3x$. Combining these,we get $-3 \cot x - \frac{2}{3} \cos 3x + c$. Factoring out the negative sign,we get $-(3 \cot x + \frac{2}{3} \cos 3x) + c$.

$\int (3 \csc^2 x + 2 \sin 3x) \, dx = $

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