## EXERCISE 1.4

#### Page No 315:

#### Question 1:

#### Answer:

Let *x*^{3} = *t*

∴ 3*x*^{2} *dx* = *dt*

#### Question 2:

#### Answer:

Let 2*x* = *t*

∴ 2*dx* = *dt*

#### Question 3:

#### Answer:

Let 2 − *x *= *t*

⇒ −*dx* = *dt*

#### Question 4:

#### Answer:

Let 5*x* =* t*

∴ 5*dx* = *dt*

#### Question 5:

#### Answer:

#### Question 6:

#### Answer:

Let *x*^{3} = *t*

∴ 3*x*^{2} *dx* = *dt*

#### Question 7:

#### Answer:

From (1), we obtain

#### Question 8:

#### Answer:

Let *x*^{3} = *t*

⇒ 3*x*^{2} *dx* = *dt*

#### Question 9:

#### Answer:

Let tan *x* =* t*

∴ sec^{2}*x* *dx* = *dt*

#### Page No 316:

#### Question 10:

#### Answer:

#### Question 11:

19×2+6x+5

#### Answer:

∫19×2+6x+5dx=∫13x+12+22dx

Let (3x+1)=t

∴

3 dx=dt

⇒∫13x+12+22dx=13∫1t2+22dt

=13×2tan-1t2+C

=16tan-13x+12+C

#### Question 12:

#### Answer:

#### Question 13:

#### Answer:

#### Question 14:

#### Answer:

#### Question 15:

#### Answer:

#### Question 16:

#### Answer:

Equating the coefficients of *x* and constant term on both sides, we obtain

4*A* = 4 ⇒ *A* = 1

*A* + *B* = 1 ⇒ *B* = 0

Let 2*x*^{2} + *x* − 3 = *t*

∴ (4*x* + 1) *dx *= *dt*

#### Question 17:

#### Answer:

Equating the coefficients of *x* and constant term on both sides, we obtain

From (1), we obtain

From equation (2), we obtain

#### Question 18:

#### Answer:

Equating the coefficient of *x* and constant term on both sides, we obtain

Substituting equations (2) and (3) in equation (1), we obtain

#### Question 19:

#### Answer:

Equating the coefficients of *x* and constant term, we obtain

2*A* = 6 ⇒ *A* = 3

−9*A* + *B* = 7 ⇒ *B* = 34

∴ 6*x* + 7 = 3 (2*x* − 9) + 34

Substituting equations (2) and (3) in (1), we obtain

#### Question 20:

#### Answer:

Equating the coefficients of *x* and constant term on both sides, we obtain

Using equations (2) and (3) in (1), we obtain

#### Question 21:

#### Answer:

Let *x*^{2} + 2*x* +3 = *t*

⇒ (2*x* + 2) *dx* =*dt*

Using equations (2) and (3) in (1), we obtain

#### Question 22:

#### Answer:

Equating the coefficients of *x* and constant term on both sides, we obtain

Substituting (2) and (3) in (1), we obtain

#### Question 23:

#### Answer:

Equating the coefficients of *x* and constant term, we obtain

Using equations (2) and (3) in (1), we obtain

#### Question 24:

equals

**A.** *x* tan^{−1} (*x* + 1) + C

**B.** tan^{− 1} (*x* + 1) + C

**C.** (*x* + 1) tan^{−1} *x* + C

**D. **tan^{−1}* x* + C

#### Answer:

Hence, the correct answer is B.

#### Question 25:

equals

**A.**

**B.**

**C.**

**D. **

#### Answer:

Hence, the correct answer is B.