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QUESTION: 1

Solution:

QUESTION: 2

Solution:

QUESTION: 3

is equal to

Solution:

QUESTION: 4

Solution:

QUESTION: 5

Solution:

QUESTION: 6

is equal to

Solution:

QUESTION: 7

where

Solution:

QUESTION: 8

The value of the integral

Solution:

QUESTION: 9

is equal to

Solution:

QUESTION: 10

is equal to

Solution:

QUESTION: 11

if

Solution:

QUESTION: 12

sin x log (sec x + tan x ) dx = f ( x ) + x + c then f (x ) =

Solution:

QUESTION: 13

The value of equal to

Solution:

and using the formula

QUESTION: 14

Solution:

QUESTION: 15

Solution:

QUESTION: 16

Solution:

QUESTION: 17

Solution:

QUESTION: 18

if then

Solution:

QUESTION: 19

Solution:

QUESTION: 20

if A tan-1 x+ Btan-1 x/2+c, then B=

Solution:

QUESTION: 21

Atan-1 x +Btan-1 x/2+c ,then ( A,B )

Solution:

So, A = 1/3 & B = 1/3

QUESTION: 22

IF

Solution:

Apply u−substitution: u = x+2

Apply the Sum Rule:

∫f(x) ± g(x)dx = ∫f(x)dx ± ∫ g(x)dx

Substitute back u=x+2

Simplify

QUESTION: 23

equal to

Solution:

QUESTION: 24

Solution:

Put x + 1=t^{3}

QUESTION: 25

Solution:

QUESTION: 26

Solution:

QUESTION: 27

equals

Solution:

QUESTION: 28

if

Solution:

Put a ^{2} cos^{2} x + b^{2 }sin ^{2} x= t

QUESTION: 29

Solution:

Put U = x, V = tax sec^{2} x

QUESTION: 30

Solution:

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