Mathematics

Evaluate $$\displaystyle\int { \cfrac { 2\cos { x } -3\sin { x }  }{ 6\cos { x } +4\sin { x }  }  } dx$$


SOLUTION
Given integral is written as $$\dfrac{1}{2}\displaystyle\int\dfrac{2cosx-3sinx}{3cosx+2sinx}$$. The integral is of the form $$\displaystyle\int \dfrac{f'(x)}{f(x)}dx=ln|f(x)|+C$$
Therefore, $$\dfrac{1}{2}\displaystyle\int\dfrac{2cosx-3sinx}{3cosx+2sinx}=\dfrac{1}{2}ln|3cosx+2sinx|+C$$
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Subjective Medium Published on 17th 09, 2020
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