Mathematics

Solve : $$\displaystyle \int \dfrac{1}{\sqrt{7 - 6x - x^2}} dx$$


SOLUTION
$$\displaystyle\int \dfrac{1}{\sqrt{7-6x-x^2}}dx$$

$$=\displaystyle\int \dfrac{1}{\sqrt{-(x+3)^2+16}}dx$$

substitute $$u=x+3\Rightarrow du=dx$$

$$=\displaystyle\int \dfrac{1}{\sqrt{-u^2+16}}du$$

$$=\sin^{-1}\dfrac{1}{4}(u)$$

$$\displaystyle\int \dfrac{1}{\sqrt{7-6x-x^2}}dx=\sin^{-1}\dfrac{1}{4}(x+3)+C$$
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Subjective Medium Published on 17th 09, 2020
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