NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.5

Question 1.
$\frac { x }{ (x+1)(x+2) }$
Solution:
NCERT Solutions Maths Class 12 Ex 7.5 Q 1
Question 2.
$\frac { 1 }{ { x }^{ 2 }-9 }$
Solution:

Question 3.
$\frac { 3x-1 }{ (x-1)(x-2)(x-3) }$
Solution:

Question 4.
$\frac { x }{ (x-1)(x-2)(x-3) }$
Solution:

Question 5.
$\frac { 2x }{ { x }^{ 2 }+3x+2 }$
Solution:
Chapter 7 Class 12 Maths Ex 7.5 Q 5
Question 6.
$\frac { 1-{ x }^{ 2 } }{ x(1-2x) }$
Solution:

Question 7.
$\frac { x }{ \left( { x }^{ 2 }+1 \right) \left( x-1 \right) }$
Solution:

Question 8.
$\frac { x }{ { \left( x-1 \right) }^{ 2 }\left( x+2 \right) }$
Solution:
Class 12 Integration NCERT Solutions Ex 7.5 Q 8
Question 9.
$\frac { 3x+5 }{ { x }^{ 3 }-{ x }^{ 2 }-x+1 }$
Solution:

Question 10.
$\frac { 2x-3 }{ ({ x }^{ 2 }-1)(2x+3) }$
Solution:

Question 11.
$\frac { 5x }{ (x-1)({ x }^{ 2 }-4) }$
Solution:

Question 12.
$\frac { { x }^{ 3 }+x+1 }{ { x }^{ 2 }-1 }$
Solution:
Class 12 Integration NCERT Solutions Ex 7.5 Q 12
Question 13.
$\frac { 2 }{ (1-x)(1+{ x }^{ 2 }) }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Miscellaneous Exercise Q 13
Question 14.
$\frac { 3x-1 }{ { (x+2) }^{ 2 } }$
Solution:

Question 15.
$\frac { 1 }{ { x }^{ 4 }-1 }$
Solution:

Question 16.
$\frac { 1 }{ x({ x }^{ n }+1) }$
[Hint : multiply numerator and denominator by x^n-1 and put xⁿ = t ]
Solution:
Class 12 Maths Ex 7.5 Q 16
Class 12 Maths Ex 7.5 Q 16 - i
Question 17.
$\frac { cosx }{ (1-sinx)(2-sinx) }$
Solution:
Class 12 Maths Ex 7.5 Q 17
Question 18.
$\frac { \left( { x }^{ 2 }+1 \right) \left( { x }^{ 2 }+2 \right) }{ \left( { x }^{ 2 }+3 \right) \left( { x }^{ 2 }+4 \right) }$
Solution:
Class 12 Maths Ex 7.5 Q 18
Class 12 Maths Ex 7.5 Q 18 - i
Question 19.
$\frac { 2x }{ ({ x }^{ 2 }+1)({ x }^{ 2 }+3) }$
Solution:
NCERT Class 12 Maths Ex 7.5 Q 19
Question 20.
$\frac { 1 }{ x({ x }^{ 4 }-1) }$
Solution:

Question 21.
$\frac { 1 }{ { e }^{ x }-1 }$
Solution:

Question 22.
choose the correct answer in each of the following :
$\int { \frac { xdx }{ (x-1)(x-2) } equals }$
(a) $log\left| \frac { { (x-1) }^{ 2 } }{ x-2 } \right| +c$
(b) $log\left| \frac { { (x-2) }^{ 2 } }{ x-1 } \right| +c$
(c) $log\left| \left( \frac { x-{ 1 }^{ 2 } }{ x-2 } \right) \right| +c$
(d) log|(x-1)(x-2)|+c
Solution:
NCERT Class 12 Maths Ex 7.5 Q 22
Question 23.
$\int { \frac { dx }{ x({ x }^{ 2 }+1) } equals }$
(a) $log|x|-\frac { 1 }{ 2 } log({ x }^{ 2 }+1)+c$
(b) $log|x|+\frac { 1 }{ 2 } log({ x }^{ 2 }+1)+c$
(c) $-log|x|+\frac { 1 }{ 2 } log({ x }^{ 2 }+1)+c$
(d) $\frac { 1 }{ 2 } log|x|+log({ x }^{ 2 }+1)+c$
Solution:
NCERT Class 12 Maths Ex 7.5 Q 23