int (2sin x + frac{1}{x}) , dx is equal to | vedclass

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Question

(A) To evaluate the integral $\int (2\sin x + \frac{1}{x}) \, dx$,we use the linearity property of integration:$\int (2\sin x + \frac{1}{x}) \, dx = \

Vedclass · Accepted Answer

$-2\cos x + \log |x| + c$

Vedclass · Answer

(A) To evaluate the integral $\int (2\sin x + \frac{1}{x}) \, dx$,we use the linearity property of integration:$\int (2\sin x + \frac{1}{x}) \, dx = \int 2\sin x \, dx + \int \frac{1}{x} \, dx$We know that $\int \sin x \, dx = -\cos x + c_1$ and $\int \frac{1}{x} \, dx = \log |x| + c_2$.Therefore,$\int 2\sin x \, dx + \int \frac{1}{x} \, dx = 2(-\cos x) + \log |x| + c = -2\cos x + \log |x| + c$.Thus,the correct option is $A$.

$\int (2\sin x + \frac{1}{x}) \, dx$ is equal to

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