NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.4

Question 1.
$\frac { { 3x }^{ 2 } }{ { x }^{ 6 }+1 }$
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 1
Question 2.
$\frac { 1 }{ \sqrt { 1+{ 4x }^{ 2 } } }$
Solution:

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

Question 4.
$\frac { 1 }{ \sqrt { 9-{ 25x }^{ 2 } } }$
Solution:

Question 5.
$\frac { 3x }{ 1+{ 2x }^{ 4 } }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 5
Question 6.
$\frac { { x }^{ 2 } }{ 1-{ x }^{ 6 } }$
Solution:

Question 7.
$\frac { x-1 }{ \sqrt { { x }^{ 2 }-1 } }$
Solution:

Question 8.
$\frac { { x }^{ 2 } }{ \sqrt { { x }^{ 6 }+{ a }^{ 6 } } }$
Solution:

Question 9.
$\frac { { sec }^{ 2 }x }{ \sqrt { { tan }^{ 2 }x+4 } }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 9
Question 10.
$\frac { 1 }{ \sqrt { { x }^{ 2 }+2x+2 } }$
Solution:

Question 11.
$\frac { 1 }{ { 9x }^{ 2 }+6x+5 }$
Solution:
miscellaneous exercise on chapter 7 class 12 Q 11
Question 12.
$\frac { 1 }{ \sqrt { 7-6x-{ x }^{ 2 } } }$
Solution:

Question 13.
$\frac { 1 }{ \sqrt { (x-1)(x-2) } }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 13
Question 14.
$\frac { 1 }{ \sqrt { 8+3x-{ x }^{ 2 } } }$
Solution:
miscellaneous exercise on chapter 7 class 12 Q 14
Question 15.
$\frac { 1 }{ \sqrt { (x-a)(x-b) } }$
Solution:

Question 16.
$\frac { 4x+1 }{ \sqrt { { 2x }^{ 2 }+x-3 } }$
Solution:
Class 12 Maths Solutions Ex 7.4 Q 16
Question 17.
$\frac { x+2 }{ \sqrt { { x }^{ 2 }-1 } }$
Solution:

Question 18.
$\frac { 5x-2 }{ 1+2x+{ 3x }^{ 2 } }$
Solution:
put 5x-2=A $\frac { d }{ dx }$ (1+2x+3x²)+B
⇒ 6A=5, A= $\frac { 5 }{ 6 }-2=2A+B$ , B= $-\frac { 11 }{ 3 }$
NCERT Solutions for Class 12 Maths Chapter 7 Integrals 18

Question 19.
$\frac { 6x+7 }{ \sqrt { (x-5)(x-4) } }$
Solution:
Class 12 Maths Solutions Ex 7.4 Q 18

Question 20.
$\frac { x+2 }{ \sqrt { 4x-{ x }^{ 2 } } }$
Solution:

Question 21.
$\frac { x+2 }{ \sqrt { { x }^{ 2 }+2x+3 } }$
Solution:

Question 22.
$\frac { x+3 }{ { x }^{ 2 }-2x-5 }$
Solution:
NCERT Maths Class 12 Ex 7.4 Q 21

Question 23.
$\frac { 5x+3 }{ \sqrt { { x }^{ 2 }+4x+10 } }$
Solution:

Question 24.
$\int { \frac { dx }{ { x }^{ 2 }+2x+2 } equals }$
(a) xtan^-1(x+1)+c
(b) (x+1)tan^-1x+c
(c) tan^-1(x+1)+c
(d) tan^-1x+c
Solution:

Question 25.
$\int { \frac { dx }{ \sqrt { 9x-{ 4x }^{ 2 } } } equals }$
(a) $\frac { 1 }{ 9 } { sin }^{ -1 }\left( \frac { 9x-8 }{ 8 } \right) +c$
(b) $\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 8x-9 }{ 9 } \right) +c$
(c) $\frac { 1 }{ 3 } { sin }^{ -1 }\left( \frac { 9x-8 }{ 8 } \right) +c$
(d) ${ sin }^{ -1 }\left( \frac { 9x-8 }{ 9 } \right) +c$
Solution:
NCERT Maths Class 12 Ex 7.4 Q 24