Integration by Reduction Formulae - Indefinite Integration, Class 12, Maths Class 12 Notes | EduRev
Class 12 : Integration by Reduction Formulae - Indefinite Integration, Class 12, Maths Class 12 Notes | EduRev
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F. INTEGRATION BY REDUCTION FORMULAE
Ex.47 
Sol.
Ex.48 Integration of 1/(x2 + k)n.
Sol.
Above is the reduction formula for 
[1/(x2 + k)n]dx . By repeated application of this formula the integral shall reduce to that of 
Ex.49 Integrate (x + 2) / (2x2 + 4x + 3)2.
Sol. Here (d/dx) (2x2 + 4x + 3) = 4x + 4.
Now put x + 1 = t and then applying the reduction formula, we get
Ex.50 Integrate (2x + 3)/(x2 + 2x + 3)2.
Sol. Here (d/dx) (x2 + 2x + 3) = 2x + 2
Ex.51 If Im=
Sol.
Ex.52 If Im,n = 
Sol. We have, Im,n = 
cosm x.cosnx dx
As we have cos (n – 1) x = cos nx cos x + sin nx . sinx
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