Question

$\int \: \dfrac{ {sin}^{2} x}{ {3cos}^{2} x + {sin}^{2} x}$​

Answer 1

Solving Steps

Evaluate the integral of

$\sf{\int \: \dfrac{ {sin}^{2} x}{ {3 \: cos}^{2} x + {sin}^{2} x}}:$

$\sf{\downarrow}$

$\sf{\int \frac{ {sin}^{2} (x)}{ {3 \: cos}^{2} (x)+ {sin}^{2} (x)}dx} = - \frac{x}{2} - \frac{ \sqrt{3} \: arctan \: ( \frac{ \sqrt{3} \: cos(x) }{sin (x)}) }{2}$

+C, C∈R

Answer 2

Answer:

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