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`int(e^(-x//2)sqrt(1-sinx))/(1+cosx)dx` का मान ज्ञात कीजिए । |
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Answer» माना `t=-x/2rArr x=-2t` `rArr dx=-2dt` `:.int(e^(-x//2)sqrt(1-sinx))/(1+cosx)dx=int(e^tsqrt(1-sin(-2t)))/(1+cos(-2t))(-2)dt` `=-2(e^tsqrt(1+sinx))/(1+cosx)dt=-2inte^t(cost+sint)/(2cos^2t)dt` `=-inte^t(sect+sect tant)dt` जहाँ `f(t)=sect` `=-e^tf(t)+c=-e^tsect+c` ` =e^(-x//2)sec.((-x)/2)+c=-e^(-x//2)sec.(x)/2+c` |
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