Mathematics

Solve 
$$\dfrac{1}{2}\int{\dfrac{(-4+2x)}{\sqrt{5-4x+x^{2}}}}$$


SOLUTION
$$\dfrac{1}{2}\int{\dfrac{(-4+2x)}{\sqrt{5-4x+x^{2}}}}dx$$

Let,  $$5-4x+x^2=t$$

$$\implies(-4+2x)dx=dt$$

$$\implies\dfrac{1}{2}\int{\dfrac{dt}{\sqrt{t}}}$$

$$\implies \dfrac{2\sqrt t}{2}+C$$

$$\implies \sqrt{5-4x+x^2}+C$$
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Subjective Medium Published on 17th 09, 2020
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