# NCERT solution class 12 chapter 1 Integrals exercise 1.2 mathematics part 2

## EXERCISE 1.2

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

Let ax + b = t

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=dtNow, 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.