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

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.

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

### (i) ∫ x4 dx

Solution:

∫ x4 dx = x4+1/(4+1) + Constant

= x5/5 + C

### (ii) ∫ x5/4 dx

Solution:

∫ x5/4 dx = x5/4 + 1/(5/4 +1) + Constant

= 4/9 x9/4 + C

### (iii) ∫ 1/x5 dx

Solution:

∫ 1/x5 dx = ∫ x-5 dx

= x-5+1/(-5+1) + Constant

= x-4/(-4)+ C

= -1/(4x4) + C

### (iv) ∫ 1/x3/2 dx

Solution:

∫ x-3/2 dx = x-3/2 + 1/(-3/2 +1) + Constant

= x-1/2/(-1/2) + C

= -2/(√x)+ C

### (v) ∫ 3x dx

Solution:

∫ 3x dx = 3x/log3 + Constant

### (vi) ∫ 1/x2/3 dx

Solution:

∫ 1/x2/3 dx = ∫ x-2/3 dx

= x-2/3 + 1/(-2/3+1) + Constant

= x1/3/(1/3) + C

= 3x1/3 + C

### (vii) ∫ 32log3 x dx

Solution:

∫ 32log3 x dx = = ∫ x2 dx

= x2+1/(2+1) + Constant

= x3/3 + C

### (i) Solution: We know, cos 2x = 2cos2 x – 1

= = ∫cos x dx

= sin x + Constant

### (ii) Solution: We know, cos 2x = 1 – 2sin2 x = ∫ sin x dx

= -cos x + Constant

### Question 3. Evaluate Solution: dx We know, e loge x = x = ∫ x2 dx

= x2+1/2+1 + Constant

= x3/3 + C

### Question 4. Evaluate: Solution: = ∫ a-x b-x dx

= ∫ (ab)-x dx

= (ab)-x/loge (ab)-1 + Constant

= -a-x b-x/loge (ab) + C

or

= -a-x b-x/ ln(ab) + C

### (i) Solution: We know, cos 2x = 1 – 2sin2 x

= ∫ 1/sin2x dx = ∫ cosec2x dx

= -cot x + Constant

### (ii) Solution:

We know, cos 2x = 2cos2 x – 1

= ∫ 1/cos2 x dx = ∫ sec2 x dx

= tan x + Constant

### Question 6. Evaluate: ∫ elog√x /x  dx

Solution:

∫ eloge √x /x dx = ∫√x/x dx

= ∫ x-1/2 dx = x-1/2 + 1/(-1/2 + 1) + Constant

= x1/2 /(1/2) + C

= 2√x + C

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