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integrate 1/((a^2)*(secx)^2+b^2)^0.5 with respect to x


integrate 1/((a^2)*(secx)^2+b^2)^0.5 with respect to x

Grade:Upto college level

2 Answers

vikas askiitian expert
509 Points
10 years ago

I= dx/[ a2 sec2x + b2 ]

 =sec2xdx/(sec2x)[ a2tan2x +a2 +b2 ]                                 (multiplying sividing by sec2x1+

 =sec2xdx/a(1+tan2x)[ tan2x + (a2 +b2 /a2) ]

put tanx =t

   sec2xdx =dt

after substituting these

 I=dt/a(1+t2)[t2 + (a2 +b2 /a2 ) ]

now integrate by using partial fraction & get ur ans

Aniket Patra
48 Points
10 years ago

Check its derivative w.r.t to x...

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