use trigonometric formulae to change (sin x)^2 = 1 - (cos x)^2 so that the intergral is completely in terms of (cos x)^2 .
Now try to write the numerator in terms of the denominator.
introduce a (-3 ) in the numerator and denominator and add and subtract 4
split it into two terms and then two integrals
The second integral contains (cos x)^2 .
divide each term with (cos x)^2 to get (sec x)^2
use trigonometric formulae tochange (sec x)^2 = 1+ (tan x)^2 in the denominator only
use substitution t = tan x and change the limits.
formulae on integration
PAGE 1 BASIC INTEGRATION
PAGE 2 INTEGRATION BY SUBSTITUTION
PAGE 3 INTEGRATION BY COMPLETION OF SQUARES
PAGE 4 INTEGRATION BY PARTS
PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR
PAGE 6 INTEGRATION USING PARTIAL FRACTIONS
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