**Chapter 3 Indefinite Integration Miscellaneous Exercise 3**

## Chapter 3 Indefinite Integration Miscellaneous Exercise 3

**I. Choose the correct options from the given alternatives:**

**Question 1.**

**Question 2.**

**Question 3.**
(a) log(3x) – log(9x) + c

(b) log(x) – (log 3) . log(log 9x) + c

(c) log 9 – (log x) . log(log 3x) + c

(d) log(x) + log(3) . log(log 9x) + c

**Answer:**

(b) log(x) – (log 3) . log(log 9x) + c

**Question 6.**

**Question 7.**

**Question 8.**

**Question 9.**

**Question 10.**

**Question 11.**

**Question 13.**

**Question 14.**

**Question 15.**

(a) sin 2x + c

(b) cos 2x + c

(c) tan 2x + c

(d) 2 sin 2x + c

**Answer:**

(a) sin 2x + c

**Question 16.**

**Question 17.**

**Question 18.∫[sin(log x) + cos(log x)] . dx =**

(a) x cos(log x) + c

(b) sin(log x) + c

(c) cos(log x) + c

(d) x sin(log x) + c

**Answer:**

(d) x sin(log x) + c

**Question 19.**

(a) tan x – x + c

(b) x + tan x + c

(c) x – tan x + c

(d) -x – cot x + c

**Answer:**

(c) x – tan x + c

**Question 20.**

**II. Integrate the following with respect to the respective variable:**

**Question 1.Solution:**

**Question 2. Solution:**

**Question 3.Solution:**

**Question 4.Solution:**

**Question 5.Solution:**

**Question 6.Solution:**

**Question 7.cos 3x cos 2x cos xSolution:**

**Question 8.Solution:**

**Question 9.**

**III. Integrate the following w.r.t. x:**

**Question 1.Solution:**

**Question 2.Solution:**

**Question 3.Solution:**

**Question 4.Solution:**

**Question 5.Solution:**

**Question 6.Solution:**

**Question 7.Solution:**

**Question 8.Solution:**

**Question 9.Solution:**

**Question 10.Solution:**

**Question 11.Solution:**

**Question 12.Solution:**

**Question 13.Solution:**

**Question 14.Solution:**

**Question 15.Solution:**

**Question 16.Solution:**

**Question 17.Solution:**

**Question 18.Solution:**

**Question 19.Solution:**

**Question 20.Solution:**