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∫(tanx)^5.(secx)^3 dx=∫(tanx)^4.(secx)^2 d(secx)=∫[(secx)^2-1]^2.(secx)^2 d(secx)=∫[(secx)^6-2(secx)^4+(secx)^2] d(secx)=(1/7)(secx)^7-(2/5)(secx)^4 +(1/3)(secx)^3 + C
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