Subjective Type

Find the integral of $$\displaystyle \int \frac {2-3 \sin x}{\cos^2x}dx$$

Solution

$$\displaystyle \int \frac {2-3 \sin x}{\cos^2x}dx$$

$$\displaystyle =\int \left (\frac {2}{\cos^2x}-\frac {3 \sin x}{\cos^2x}\right )dx$$

$$\displaystyle =\int 2 \sec^2x dx-3\int \tan x \sec x dx$$

$$=2 \tan x-3 \sec x+C$$

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