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# Integrate the function: $\int \frac{\large 2cos\: x-3sin\: x}{\large 6cos\: x+4sin\: x}$

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## 1 Answer

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Toolbox:
• (i)Method of substitution :
• Given f(x)dx can be transformed into another form by changing independent variable x to t by substituting x=g(t).
• Consider $I=\int f(x)dx.$
• Put x=g(t) so that $\frac{dx}{dt}=g'(t).$
• $\Rightarrow$dx=g'(t)dt.
• Thus $I=\int f(g(t).g'(t))dt.$
• (ii)$\int \sin xdx=-\cos x.$