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$\int \frac{1}{(2 x-7) \sqrt{x^2-7 x+12}} d x$ is equal to |
$2 \sec ^{-1}(2 x-7)+C$ $\sec ^{-1}(2 x-7)+C$ $\frac{1}{2} \sec ^{-1}(2 x-7)+C$ none of these |
$\sec ^{-1}(2 x-7)+C$ |
Let $I=\int \frac{1}{(2 x-7) \sqrt{x^2-7 x+12}} d x$ $\Rightarrow I=\int \frac{2}{(2 x-7) \sqrt{4 x^2-28 x+48}} d x$ $\Rightarrow I=\int \frac{1}{(2 x-7) \sqrt{(2 x-7)^2-12}} d(2 x-7)=\sec ^{-1}(2 x-7)+C$ |
