Here we provide RD Sharma Class 12 Ex 19.1 Solutions Chapter 19 Indefinite Integrals for English medium students, Which will very helpful for every student in their exams. Students can download the latest Sharma Class 12 Ex 19.1 Solutions Chapter 19 Indefinite Integrals book pdf download. Now you will get step-by-step solutions to each question.

Textbook | NCERT |

Class | Class 12th |

Subject | Maths |

Chapter | 19 |

Exercise | 19.1 |

Category | RD Sharma Solutions |

Table of Contents

**RD Sharma Class 12 Ex 19.1 Solutions Chapter 19 Indefinite Integrals**

### Question 1. Integrate the following integrals with respect to x:

### (i) ∫ x^{4} dx

**Solution:**

∫ x

^{4}dx = x^{4+1}/(4+1) + Constant= x

^{5}/5 + C

### (ii) ∫ x^{5/4} dx

**Solution:**

∫ x

^{5/4}dx = x^{5/4 + 1}/(5/4 +1) + Constant= 4/9 x

^{9/4}+ C

### (iii) ∫ 1/x^{5} dx

**Solution:**

∫ 1/x

^{5}dx = ∫ x^{-5}dx= x

^{-5+1}/(-5+1) + Constant= x

^{-4}/(-4)+ C= -1/(4x

^{4}) + C

### (iv) ∫ 1/x^{3/2} dx

**Solution:**

∫ x

^{-3/2}dx = x^{-3/2 + 1}/(-3/2 +1) + Constant= x

^{-1/2}/(-1/2) + C= -2/(√x)+ C

### (v) ∫ 3^{x} dx

**Solution:**

∫ 3

^{x}dx = 3^{x}/log3 + Constant

### (vi) ∫ 1/x^{2/3} dx

**Solution:**

∫ 1/x

^{2/3}dx = ∫ x^{-2/3}dx= x

^{-2/3 + 1}/(-2/3+1) + Constant= x

^{1/3}/(1/3) + C= 3x

^{1/3}+ C

### (vii) ∫ 3^{2log}_{3}^{ x} dx

**Solution:**

∫ 3

^{2log}_{3}^{ x}dx == ∫ x

^{2}dx= x

^{2+1}/(2+1) + Constant= x

^{3}/3 + C

### Question 2. Evaluate

### (i)

**Solution:**

=

We know, cos 2x = 2cos^{2} x – 1

=

= ∫cos x dx

= sin x + Constant

### (ii)

**Solution:**

=

We know, cos 2x = 1 – 2sin^{2} x

=

= ∫ sin x dx

= -cos x + Constant

### Question 3. Evaluate

**Solution:**

dx

=

We know, e

^{log}_{e}^{ x}= x=

= ∫ x

^{2}dx= x

^{2+1}/2+1 + Constant= x

^{3}/3 + C

### Question 4. Evaluate:

**Solution:**

= ∫ a

^{-x}b^{-x}dx= ∫ (ab)

^{-x}dx= (ab)

^{-x}/log_{e}(ab)^{-1}+ Constant= -a

^{-x}b^{-x}/log_{e}(ab) + Cor

= -a

^{-x}b^{-x}/ ln(ab) + C

### Question 5. Evaluate

### (i)

**Solution:**

=

We know, cos 2x = 1 – 2sin^{2} x

= ∫ 1/sin^{2}x dx = ∫ cosec^{2}x dx

= -cot x + Constant

### (ii)

**Solution:**

We know, cos 2x = 2cos^{2} x – 1

= ∫ 1/cos^{2}_{ }x dx = ∫ sec^{2} x dx

= tan x + Constant

### Question 6. Evaluate: ∫ e^{log√x} /x dx

**Solution:**

∫ e

^{log}_{e}^{ √x}/x dx = ∫√x/x dx= ∫ x

^{-1/2}dx = x^{-1/2 + 1}/(-1/2 + 1) + Constant= x

^{1/2}/(1/2) + C= 2√x + C

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