Mathematics

Evaluate : $$\int { \sqrt { \dfrac { x }{ { x }^{ 3 }{ a }^{ 3 } }  } dx } $$


SOLUTION
Consider the given integral.
$$I=\int \sqrt{\dfrac{x}{x^3a^3}}dx$$
$$I=\int \sqrt{\dfrac{1}{x^2a^3}}dx$$
$$I={\dfrac{1}{a\sqrt a}}\int \dfrac{1}{x} dx$$
$$I={\dfrac{1}{a\sqrt a}} log_e x+C$$

Hence, this is the answer.
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Subjective Medium Published on 17th 09, 2020
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