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Determine-the-results-of-the-following-I-1-a-e-x-a-e-x-dx-I-2-tanx-tanx-1-tan-2-x-dx-




Question Number 907 by Yugi last updated on 19/Apr/15
Determine the results of the following.                   I_1 =∫(√((a+e^x )/(a−e^x )))dx                  I_2 =∫(((tanx)∣tanx∣)/(1−tan^2 x))dx
Determinetheresultsofthefollowing.I1=a+exaexdxI2=(tanx)tanx1tan2xdx
Commented by prakash jain last updated on 21/Apr/15
I_1   e^x =acos t  e^x dx=−asin t dt  dx=−tan t dt  ∫−tan t (1/(tan (t/2))) dt  =−∫(2/(1−tan^2 t/2)) dt=−∫(sec t+1)dt  =−t−ln (sec t+tan t)+C  where t=cos^(−1) (e^x /a)
I1ex=acostexdx=asintdtdx=tantdttant1tant2dt=21tan2t/2dt=(sect+1)dt=tln(sect+tant)+Cwheret=cos1exa

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