InterviewSolution
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InterviewSolution
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`int(1)/((1tan x))dx` का मान ज्ञात कीजिए। |
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Answer» माना `I = int (1)/((1+tanx)) dx = int(1)/((1+(sinx)/(cosx))) dx` ` = int (1)/(((cosx + sinx)/(cosx)))dx = int(cosx)/((cosx + sinx))dx` ` =int ((cos x + sinx)+(cosx-sinx))/(2(cos x+sinx))dx` ` = (1)/(2)int((cosx + sinx))/((cos x+sinx))dx +(1)/(2)int((cosx - sinx))/((cos x + sinx))dx` ` = (1)/(2)int dx + (1)/(2)int((cos x - sin))/((cos x + sinx))dx` यदि `(cos x + sinx) = t` व `(cos x - sinx) dx = dt` अब `I = (1)/(2) int dx + (1)/(2) int(1)/(t) dt` ` =(1)/(2) x +(1)/(2)log |t| +c = (1)/(2) x +(1)/(2)log |cos x+ sin x|+c` |
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