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Integrate 5/root(x+3)-root(x-2) Kindly provide the answer …

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Integrate 5/root(x+3)-root(x-2)

Kindly provide the answer for the above question

Posted by Srinivas Chandra 6 years, 10 months ago

CBSE > Class 12 > Mathematics

1 answers

Naveen Sharma 6 years, 10 months ago

Ans.

{tex}\int {5\over {\sqrt {x+3} - \sqrt {x-2}}} dx{/tex} Multiply and divide by {tex}{\sqrt {x+3} + \sqrt {x-2}}{/tex}

=> {tex}\int {5\over {\sqrt {x+3}\ - \sqrt {x-2}} } \times {{\sqrt {x+3} \ + \sqrt {x-2}}\over {\sqrt {x+3} \ + \sqrt {x-2}}} dx{/tex}

=> {tex}\int{ {5( \sqrt {x+3} \ + \sqrt {x-2} )} \over x+3 - x + 2} dx{/tex}

=> {tex}\int{ {5( \sqrt {x+3} \ + \sqrt {x-2} )} \over 5} dx{/tex}

=> {tex}\int{ ({ \sqrt {x+3} \ + \sqrt {x-2} } )dx}{/tex}

=> {tex}\int{ { \sqrt {x+3} }\ dx + \int {\sqrt {x-2} } \ dx}{/tex}

=> {tex}{2\over 3}(x+3)^{3\over 2} + {2\over 3}(x-2)^{3\over 2}{/tex}

1Thank You

ANSWER

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