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निम्न फलनों का समाकलन कीजिए - `(mtan^(-1)x)/((1+x^2)^(3//2)` |
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Answer» Correct Answer - `(m(xtan^(-1)x+1))/sqrt((1+x^2))` यदि `tan^(-1)x=t rArrx=tantrArrrArr1/(1+x^2)dx=dt` `I =int(mtdt)/((1+tan^2t)^(1//2))=int(mt)/(sec^2t)^(1//2))dt` `=int(mt)/(sect)dt=intmcost. t d t` `=mint t cos t dt =m (t sint +cos t))` `t =tan^(-1) dt =int m(t sin t =cos t)) ` `t= tan^(-1)x` का प्रयोग करने पर `rArr sint =x/(sqrt(1+x^2))" व " cost =1/(sqrt(1+x^2))` |
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