Mathematics

# Integrate with respect to $\dfrac { \sqrt { { x }^{ 2 }-8 } }{ { x }^{ 4 } }$

##### SOLUTION

Consider the given integral.

$I=\int{\dfrac{x-8}{{{x}^{4}}}dx}$

$I=\int{\left( \dfrac{1}{{{x}^{3}}}-\dfrac{8}{{{x}^{4}}} \right)dx}$

$I=\int{\dfrac{1}{{{x}^{3}}}dx}-8\int{\dfrac{1}{{{x}^{4}}}dx}$

$I=-\dfrac{1}{2{{x}^{2}}}+\dfrac{8}{3{{x}^{3}}}+C$

$I=\dfrac{16-3x}{6{{x}^{3}}}+C$

Hence, this is the required value of the integral.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
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Chapters 126
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