NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.2

Let t
∴2x dx = dt

Let log |x| = t
∴

Let 1 + log t
∴

Question 4:

sin x ⋅ sin (cos x)

sin x ⋅ sin (cos x)
Let cos x = t
∴ −sin x dx = dt

Let
∴ 2adx = dt

Let ax + b = t
⇒ adx = dt

Let
∴ dx = dt

Let 1 + 2x2 = t
∴ 4xdx = dt

Question 9:

Let
∴ (2x + 1)dx = dt

Let

Question 11:

Let I=∫xx+4 dxput x+4=t⇒dx=dt
Now, I=∫t-4tdt=∫t-4t-1/2dt=23t3/2-42t1/2+C=23.t.t1/2-8t1/2+C=23x+4x+4-8x+4+C
=23xx+4+83x+4-8x+4+C=23xx+4-163x+4+C
=23x+4x-8+C

Let
∴

Let
∴ 9x2 dx = dt

Let log x = t
∴

Let
∴ −8x dx = dt

Let
∴ 2dx = dt

Let
∴ 2xdx = dt

Let
∴

Question 19:

Dividing numerator and denominator by ex, we obtain
Let
∴

Let
∴

Question 21:

Let 2x − 3 = t
∴ 2dx = dt
⇒∫tan22x-3dx = ∫sec22x-3 – 1dx=∫sec2t- 1dt2= 12∫sec2t dt – ∫1dt= 12tant – t + C= 12tan2x-3 – 2x-3 + C

Let 7 − 4x = t
∴ −4dx = dt

Let
∴

Let
∴

Let
∴

Let
∴

Let sin 2x = t
∴

Let
∴ cos x dx = dt

Question 29:

cot x log sin x

Let log sin x = t

Question 30:

Let 1 + cos x = t
∴ −sin x dx = dt

Question 31:

Let 1 + cos x = t
∴ −sin x dx = dt

Question 32:

Let sin x + cos x = t ⇒ (cos x − sin xdx = dt

Question 33:

Put cos x − sin x = t ⇒ (−sin x − cos xdx = dt

Question 35:

Let 1 + log x = t
∴

Let
∴

Question 37:

Let x4 = t
∴ 4x3 dx = dt
Let
From (1), we obtain

Question 38:

equals

Let
∴
Hence, the correct answer is D.

equals
A.
B.
C.
D.