NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.2

NCERT Solutions for Class 12 Maths Chapter 7 Integrals
Integrate the functions in Exercises 1 to 37:

Question 1.
$\frac { 2x }{ 1+{ x }^{ 2 } }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 Q 1
Question 2.
$\frac { { \left( logx \right) }^{ 2 } }{ x }$
Solution:

Question 3.
$\frac { 1 }{ x+xlogx }$
Solution:

Question 4.
sinx sin(cosx)
Solution:
ncert solutions class 12 maths Chapter 7 Integrals Ex 7.2 Q 4
Question 5.
sin(ax+b) cos(ax+b)
Solution:
class 12 integration NCERT Solutions Chapter 7 Ex 7.2 Q 5
Question 6.
$\sqrt { ax+b }$
Solution:

Question 7.
$x\sqrt { x+2 }$
Solution:

Question 8.
$x\sqrt { 1+{ 2x }^{ 2 } }$
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 8

Question 9.
$(4x+2)\sqrt { { x }^{ 2 }+x+1 }$
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 9
Question 10.
$\frac { 1 }{ x-\sqrt { x } }$
Solution:

Question 11.
$\frac { x }{ \sqrt { x+4 } } ,x>0$
Solution:

Question 12.
${ { (x }^{ 3 }-1) }^{ \frac { 1 }{ 3 } }.{ x }^{ 5 }$
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 12
Question 13.
$\frac { { x }^{ 2 } }{ { { (2+3x }^{ 3 }) }^{ 3 } }$
Solution:

Question 14.
$\frac { 1 }{ x(logx)^{ m } } ,x>0$
Solution:

Question 15.
$\frac { x }{ 9-4{ x }^{ 2 } }$
Solution:

Question 16.
${ e }^{ 2x+3 }$
Solution:
ncert maths solutions class 12 Integration Chapter 7 Ex 7.2 Q 16
Question 17.
$\frac { x }{ { e }^{ { x }^{ 2 } } }$
Solution:

Question 18.
$\frac { { e }^{ { tan }^{ -1 }x } }{ 1+{ x }^{ 2 } }$
Solution:

Question 19.
$\frac { { e }^{ 2x }-1 }{ { e }^{ 2x }+1 }$
Solution:
integration ncert solutions Class 12 chapter 7 Ex 7.2 Q 19
Question 20.
$\frac { { e }^{ 2x }-{ e }^{ 2x } }{ { e }^{ 2x }+{ e }^{ -2x } }$
Solution:

Question 21.
tan²(2x-3)
Solution:
∫tan²(2x-3)dx = ∫[sec²(2x-3)-1]dx = I
put 2x-3 = t
so that 2dx = dt
I = $\frac { 1 }{ 2 }$ ∫sec²t dt-x+c
= $\frac { 1 }{ 2 }t-x+c$
= $\frac { 1 }{ 2 }tan(2x-3)-x+c$
Question 22.
sec²(7-4x)
Solution:
maths class 12 ncert solutions Chapter 7 Integration Ex 7.2 Q 22
Question 23.
$\frac { { sin }^{ -1 }x }{ \sqrt { 1-{ x }^{ 2 } } }$
Solution:

Question 24.
$\frac { 2cosx-3sinx }{ 6cosx+4sinx }$
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 24
Question 25.
$\frac { 1 }{ { cos }^{ 2 }x{ (1-tanx) }^{ 2 } }$
Solution:

Question 26.
$\frac { cos\sqrt { x } }{ \sqrt { x } }$
Solution:

Question 27.
$\sqrt { sin2x } cos2x$
Solution:

Question 28.
$\frac { cosx }{ \sqrt { 1+sinx } }$
Solution:
Integration Solutions class 12 Maths Chapter 7 Ex 7.2 Q 28
Question 29.
cotx log sinx
Solution:

Question 30.
$\frac { sinx }{ 1+cosx }$
Solution:

Question 31.
$\frac { sinx }{ { (1+cosx) }^{ 2 } }$
Solution:
NCERT Maths Class 12 Solutions Chapter 7 Ex 7.2 Q 31
Question 32.
$\frac { 1 }{ 1+cotx }$
Solution:

Question 33.
$\frac { 1 }{ 1-tanx }$
Solution:

Question 34.
$\frac { \sqrt { tanx } }{ sinxcosx }$
Solution:
NCERT Integration Solutions Ex 7.2 Q 34
Question 35.
$\frac { { (1+logx) }^{ 2 } }{ x }$
Solution:

Question 36.
$\frac { (x+1){ (x+logx) }^{ 2 } }{ x }$
Solution:

Question 37.
$\frac { { x }^{ 3 }sin({ tan }^{ -1 }{ x }^{ 4 }) }{ 1+{ x }^{ 8 } } dx$
Solution:

Choose the correct answer in exercises 38 and 39

Question 38.
$\int { \frac { { 10x }^{ 9 }+{ 10 }^{ x }log{ e }^{ 10 } }{ { x }^{ 10 }+{ 10 }^{ x } } dx }$
(a) 10x – x10 + C
(b) 10x + x10 + C
(c) (10x – x10) + C
(d) log (10x + x10) + C
Solution:
NCERT Integration Solutions Ex 7.2 Q 38
Question 39.
$\int { \frac { dx }{ { sin }^{ 2 }x{ \quad cos }^{ 2 }x } = }$
(a) tanx + cotx + c
(b) tanx – cotx + c
(c) tanx cotx + c
(d) tanx – cot2x + c
Solution:
NCERT Solutions for Class 12 Maths integrals Ex 7.2 Q 39