48 = 4 9 4 27 1 sin 9x 27  x c = 12 5.8 Formulae for integration when the integrand contains quadratic expressions in the denominator. x  2 2  c 1. 1 x a a tan dx a   2 a 2 2 x a x a 2. 1   dx x a c ln dx x 3. sinh  a   x a 2 2 x dx 4. cosh  a x a if x > a 2 2 if > a –x a dx x 5. x a 2 2 sin  a Example 14 x  2 2 Prove that 1 x a a tan dx a  Proof
48 = 4 9 4 27 = 1 12 sin 9x 27 x  c 5.8 Formulae for integration when the integrand contains quadratic expressions in the denominator. 1. x 2 dx  a 2  1 a tan x a  c 2. x 2 dx a 2  1 2 a ln x a x  a  c 3. 4. dx x 2  a 2 dx x 2 a 2  sinh  cosh x a x a  if x > a if –x > a a 5. dx x 2 a 2  sin x a Example 14 Prove that x 2 dx  a 2  1 a tan x a Proof
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