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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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