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B
False
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Solution
The correct option is A True Let I=∫(px+qx)2px.qx+e5logex−e4logexe3logex−e2logex+sin2x+cos2xsin2xcos2xdx ⇒I=I1+I2+I3 Where I1=∫(px+qx)2px.qxdx=∫(p2xpxqx+q2xpxqx+2pxqxpxqx)dx =∫(1qx/px+1px/qx+2)dx=(p/q)xlog(p/q)+(q/p)xlog(q/p)+2x I2=∫e5logex−e4logexe3logex−e2logexdx=∫x5−x4x3−x2dx=∫x2dx=x33 I3=∫sin2x+cos2xsin2xcos2xdx=∫(sec2x+csc2x)dx=tanx−cotx Hence I=(p/q)xlog(p/q)+(q/p)xlog(q/p)+2x+x33+tanx−cotx