Q. 244.8( 4 Votes )

Using properties

Answer :

We know,



Let


Now,













I = π


OR


Dividing numerator and denominator by cos3x




Put tanx = t, then sec2xdx = dt



By partial fractions


Let



t = At2 – At + A + Bt + Bt2 + Ct + C


t = t2(A + B) + (-A + B + C) t + A + C


On comparing, A + B = 0


-A + B + C = 1, A + C = 0


On solving, ,






Where, u = t2 – t + 1 and du = 2t – 1





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