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# 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

The document Integration by Reduction Formulae - Indefinite Integration, Class 12, Maths Class 12 Notes | EduRev is a part of Class 12 category.
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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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