Flag Integral Calculus> 1/x1/x*x1/x+1x-1/x+1 dx=______?_______ Sir,pls tell
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1/x1/x*x1/x+1x-1/x+1 dx=______?_______ Sir,pls tell me the detailed solution of this as soon as possible.thank u in advance...

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ajay govind , 8 Years ago
Grade 12th pass
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Ajay

Last Activity: 8 Years ago

Please find the answer, this could be easily solved if you know differentaition of inverse trignometric functions
∫  frac  dx  x√  x-1x+1      =quad ∫  frac  dx  x√   x ^ 2 -1     quad  Putquad x=sectheta quad soquad thatquad dxquad =quad sectheta tantheta dtheta   =quad ∫  frac  sectheta tantheta dtheta  sectheta √   sectheta ^ 2 -1    =quad ∫  frac  sectheta tantheta dtheta  sectheta √    tan ^ 2 theta       ∫  dtheta quad =quad theta quad +quad Cquad quad =quad  sec ^ -1 xquad +quad C

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