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`int sqrt((1-sinx)/((1+cosx)))e^(-x//2)dx` का मान ज्ञात कीजिए । |
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Answer» दिया है - `intsqrt((1-sinx)/((1+cosx)))e^(-x//2)dx` यदि `-x/2=trArr x=-2t" व " dx=-2dt`, तब `intsrt((1-sinx)/((1+cosx)))e^(-x//2)dx=intsqrt((1-sin(-2t))/([1+cos(-2t)]))e^t(-2dt)` `=-2intsqrt(1+sin2t)/((1+cos2t))e^tdt` `=-2intsqrt(cos^2t+sin^2t+2sint cost)/(2cos^2t)e^tdt` `=-2int((cost+sint))/(2cos^2t)e^tdt` `=-int(sect+sect tant )e^tdt` `=-inte^tf(t)+c=-e^(-x//2)sec(-x/2)+c` `=e^(-x//2)sec.(x/2)+c` |
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