NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.5

5 Integrate the rational functions in Exercises 1 to 21

Question 1:( 1) ( 2) x x x

Question 2:2 1 x – 9

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Question 3:3 1 ( 1) ( 2) ( 3) x – x – x– x–

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Question 4:( 1) ( 2) ( 3) x x – x– x–

Question 5:2 2 3 2 x x x

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Question 6:2 1 (1 2 ) – x x – x

Question 7:2 ( 1)( – 1) x x x

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Question 8:2 ( 1) ( 2) x x– x

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Question 9:3 2 3 5 1 x x –x x

Question 10:2 2 3 ( 1) (2 3) x x– x

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Question 11:2 5 ( 1) ( 4) x x x

Question 12:3 2 1 1 x x x

Question 13:2 2 (1 ) (1 ) x x

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Question 14:2 3 1 ( 2) x – x

Question 15:4 1 x 1

5 Integrate the rational functions in Exercises

Question 16:1 ( 1) n x x [Hint: multiply numerator and denominator by x n – 1 and put x n = t ]

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Question 17:cos (1 – sin ) (2 – sin ) x x x [Hint : Put sin x =

Question 18:2 2 2 2 ( 1)( 2) ( 3) ( 4) x x x x

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Question 19:2 2 2 ( 1)( 3) x x x

Question 20:4 1 x ( 1 x – )

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Question 21:1 ( 1) x e – [Hint : Put e x = t] Choose the correct answer in each of the Exercises 22 and 23

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Question 22:( 1) ( 2) x dx x x equals (A) 2 ( 1) log C 2 x x (B) 2 ( 2) log C 1 x x (C) 2 1 log C 2 x x (D) log ( 1) ( 2) C x x

Question 23:2 ( 1) dx x x equals (A) 1 2 log log ( +1) + C 2 x x (B) 1 2 log log ( +1) + C 2 x x (C) 1 2 log log ( +1) + C 2 x x (D) 1 2 log log ( +1)