InterviewSolution
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InterviewSolution
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`int(2x+5)/(sqrt(x^(2)+2x+5))dx` का मान ज्ञात कीजिए | |
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Answer» माना `I=int(2x+5)/(sqrt(x^(2)+2x+5))dx` `=int(2x+2)/(sqrt(x^(2)+2x+5))dx+int(3dx)/(sqrt((x^(2)+2x+1)+4))` माना `x^(2)+2x+5= t rArr (2x+2)dx=dt` `therefore I=int(dt)/(sqrtt)+3int(dx)/(sqrt((x+1)^(2)+4))` `=2t^(1//2)+3int(dx)/(sqrt((x+1)^(2)+4))` `=2sqrt(x^(2)+2x+5)+3 int(dx)/(sqrt(4+(x+1)^(2)))` पुनः माना `x+1=2 tan theta rArr dx=2sec^(2)theta d theta` `therefore" "I=2sqrt(x^(2)+2x+5)+3int(2sec^(2)theta d theta)/(sqrt(4+4tan^(2) theta))` `=2sqrt(x^(2)+2x+5)+3 int(sec^(2)theta)/(sec theta)d theta` `=2sqrt(x^(2)+2x+5)+3 log (sec theta+ tan theta)` `=2sqrt(x^(2)+2x+5)+3 log[sqrt(1+((x+1)/(2))^(2))+(x+1)/(2)]` `=2sqrt(x^(2)+2x+5)+3log[(sqrt(x^(2)+2x+5))/(2)+(x+1)/(2)]+c` `=2sqrt(x^(2)+2x+5)+3log[sqrt(x^(2)+2x+5)+(x-1)]+c_(1)` `" "` जहाँ `c_(1)=c-log 2` |
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