XII Maths Chapter 7. Integrals | Page 9

( ii ) Form II
Put px + q = λd / dx ( ax2 + bx + c ) + mu ; Now , find values of λ and mu ; and integrate . ( iii ) Form III
when P ( x ) is a polynomial of degree 2 or more carry out the dimension
and express in the form P ( x ) / ( ax 2 + bx + c ) = Q ( x ) + R ( x ) / ( ax 2 + bx + c ), where R ( x ) is a linear expression or constant , then integral reduces to the form discussed earlier .
( iv ) Form IV
After dividing both numerator and denominator by x 2 , put x – a 2 / x = t or x + ( a 2 / x ) = t .
( v ) Form V