1. integral left parenthesis square root of a squared plus x squared end root right parenthesis divided by x space d x
 

Asked by mahirajsingh37 | 5th Jan, 2016, 09:22: PM

Expert Answer:

bold integral fraction numerator square root of bold a to the power of bold 2 bold plus bold x to the power of bold 2 end root over denominator bold x end fraction bold italic d bold italic x bold equals bold integral fraction numerator square root of bold a to the power of bold 2 bold plus bold x to the power of bold 2 end root over denominator bold x to the power of bold 2 end fraction bold italic x bold italic d bold italic x bold italic S bold italic u bold italic b bold italic s bold italic t bold italic i bold italic t bold italic u bold italic t bold italic e bold space bold italic a to the power of bold 2 bold plus bold italic x to the power of bold 2 bold equals bold italic t to the power of bold 2 bold italic D bold italic i bold italic f bold italic f bold italic e bold italic r bold italic e bold italic n bold italic t bold italic i bold italic a bold italic t bold italic i bold italic n bold italic g bold space bold italic w bold italic e bold space bold italic g bold italic e bold italic t bold 2 bold italic x bold italic d bold italic x bold equals bold 2 bold italic t bold italic d bold italic t bold rightwards double arrow bold italic x bold italic d bold italic x bold equals bold italic t bold italic d bold italic t bold italic S bold italic o bold space bold italic t bold italic h bold italic e bold space bold italic i bold italic n bold italic t bold italic e bold italic g bold italic r bold italic a bold italic l bold space bold italic b bold italic e bold italic c bold italic o bold italic m bold italic e bold italic s bold integral fraction numerator bold t bold. bold t bold d bold t over denominator bold t to the power of bold 2 bold minus bold a to the power of bold 2 end fraction bold equals bold integral fraction numerator bold t to the power of bold 2 bold d bold t over denominator bold t to the power of bold 2 bold minus bold a to the power of bold 2 end fraction bold equals bold integral fraction numerator open parentheses bold t to the power of bold 2 bold minus bold a to the power of bold 2 bold plus bold a to the power of bold 2 close parentheses bold d bold t over denominator bold t to the power of bold 2 bold minus bold a to the power of bold 2 end fraction bold equals bold integral fraction numerator bold t to the power of bold 2 bold minus bold a to the power of bold 2 over denominator bold t to the power of bold 2 bold minus bold a to the power of bold 2 end fraction bold italic d bold italic t bold plus bold integral fraction numerator bold a to the power of bold 2 bold d bold t over denominator bold t to the power of bold 2 bold minus bold a to the power of bold 2 end fraction bold equals bold integral bold italic d bold italic t bold plus bold italic a to the power of bold 2 bold integral fraction numerator bold d bold t over denominator bold t to the power of bold 2 bold minus bold a to the power of bold 2 end fraction bold equals bold italic t bold plus bold italic a to the power of bold 2 bold cross times fraction numerator bold 1 over denominator bold 2 bold a end fraction bold italic l bold italic o bold italic g open vertical bar fraction numerator bold t bold minus bold a over denominator bold t bold plus bold a end fraction close vertical bar bold plus bold italic C bold equals bold italic t bold plus bold a over bold 2 bold italic l bold italic o bold italic g open vertical bar fraction numerator bold t bold minus bold a over denominator bold t bold plus bold a end fraction close vertical bar bold plus bold italic C bold italic R bold italic e bold italic s bold italic u bold italic b bold italic s bold italic t bold italic i bold italic t bold italic u bold italic t bold italic e bold space bold italic t bold italic h bold italic e bold space bold italic v bold italic a bold italic l bold italic u bold italic e bold space bold italic o bold italic f bold space bold apostrophe bold italic t bold apostrophe bold. bold italic S bold italic o bold space bold italic t bold italic h bold italic e bold space bold italic r bold italic e bold italic s bold italic u bold italic l bold italic t bold space bold italic i bold italic s square root of bold a to the power of bold 2 bold plus bold x to the power of bold 2 end root bold plus bold a over bold 2 bold italic l bold italic o bold italic g open vertical bar fraction numerator square root of bold a to the power of bold 2 bold plus bold x to the power of bold 2 end root bold minus bold a over denominator square root of bold a to the power of bold 2 bold plus bold x to the power of bold 2 end root bold plus bold a end fraction close vertical bar bold plus bold italic C

Answered by satyajit samal | 6th Jan, 2016, 08:03: PM

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