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Question Number 190937 by Spillover last updated on 14/Apr/23

Show  that                       ∫  ((sech (√x) tanh (√x))/( (√x)))=−(2/(cosh (√x)))

Showthatsechxtanhxx=2coshx

Answered by ARUNG_Brandon_MBU last updated on 15/Apr/23

I=∫(((sech(√x))(tanh(√x)))/( (√x)))dx=∫((sinh(√x))/( (√x)cosh^2 (√x)))dx  t=cosh(√x) ⇒dt=((sinh(√x))/(2(√x)))dx  I=∫(2/t^2 )dt=−(2/t)+C=−(2/(cosh(√x)))+C

I=(sechx)(tanhx)xdx=sinhxxcosh2xdxt=coshxdt=sinhx2xdxI=2t2dt=2t+C=2coshx+C

Commented by Spillover last updated on 15/Apr/23

great

great

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