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`int_(0)^(4)(dx)/(sqrt(x^(2)+2x+3))` का मान ज्ञात कीजिए। |
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Answer» `int_(0)^(4)(dx)/(sqrt(x^(2)+2x+3))` `=int_(0)^(4)(1)/(sqrt((x^(2)+2x+1)+2))dx` `=int_(0)^(4)(1)/(sqrt((x+1)^(2)+(sqrt2)^(2)))dx` `=[log|x+1+sqrt((x+1)^(2)+(sqrt2)^(2))|]_(0)^(4)` `=[log|x+1+sqrt(x^(2)+2x+3)|]_(0)^(4)` `=log|5+sqrt(16+8+3)|-log|1+sqrt3|` `=log|(5+3sqrt3)/(1+sqrt3)|` |
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