## 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.

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Question 7.

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Question 8.

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Question 9.

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Question 10.

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Question 11.

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Question 12.

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Question 13.

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Question 14.

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Question 15.

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Question 16.

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Question 17.

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Question 18.

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Question 19.

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Question 20.

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Question 21.

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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.

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Question 25.

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