duction is the same, excepting that both terms are negative. The final integrals to which it is reduced are

3

+

√ (a + b) = (a + b)1 ((a+ba)" - f a (a + bx) +

(11) Let the function be

dx

(a2 + x2)

8

1

n

(a2 + x2)2

n

(n-2) a2

+

(a2 + x2) - 1

2

n

a2) 3a2 (a2 + x2)§°

+

3a2 (a2 x2)

5a2 (a2

√ ( a + bx + c x ) }

"-1dx

(a + bx + cx2) *

By this the integral is made to depend on

If

dx

x dx

I (a + bx + cx2), and S (a + bx + cx2) 3

n = 2, a = b = c = 1;

x2 d x

( 1 + x + x) *

If

1

n = 3,

Let the function be ex";

2x+1

54

=

a

fe a dx = € ̄* (x2 + 5x3 + 20x3 + 60 x2 + 120 x + 120).

(15) Let the function be a (log x)" ;

fa” (log a)a da = ~= { (log x)2 – } log x + }} ·

4

fx (log x)3 dx =

2

{(log a)3

(a)3 – § (log a)2 + § (log a) – 2,3}.

(16) Let the function be (sin x)" (cos x)".

We may use any of the following formula of reduction :