RBSE Solutions for Class 12 Maths Integration Miscellaneous Exercise is part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Class 12 Maths Integration Miscellaneous Exercise.

## Rajasthan Board RBSE Class 12 Maths Integration Miscellaneous Exercise

**Integrate the following functions with respect to x :**

Question 1.

[1+2 tan x (tan x + sec x)]

Solution:

∫ [1 + 2 tan x (tan x + sec x)] dx

= ∫ [1 + 2 tan^{2} x + 2 tan x sec x] dx

= ∫ [2(1 + tan^{2} x) + 2 sec x tan x -1] dx

= 2 ∫ (sec^{2} x + sec x tan x) dx – ∫ dx

= 2(tan x + sec x) – x + C

Question 2.

e^{x} sin^{3} x

Solution:

Question 3.

x^{2} log (1 – x^{2})

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:

Question 21.

Solution:

Question 22.

(a) tan x + x + C

(b)cot x + x + C

(c) tan x – x + C

(d) cot x – x + C

Solution:

Hence correct option is (c).

Question 23.

Solution:

Question 24.

Solution:

Question 25.

Solution:

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