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Question Number 78468 by Dah Solu Tion last updated on 17/Jan/20
IfF(x)=∫0arctanxt4−1t4+1dt,findF′(x).
Commented by mathmax by abdo last updated on 17/Jan/20
wehaveF(x)=∫0arctan(x)t4−1t4+1dt⇒F(x)=∫0arctan(x)t4+1−2t4+1dt=∫0arctanx(1−2t4+1)12dtdFdx(x)=11+tan2x(1−21+tan4x)12=cos2x(1−2(1+tan2x)−2tanx)12=cos2x(1−2cos4x−2tanx)12
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