Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.4

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.4

Integrate the following functions:
Question 1.
(frac{3 x^{2}}{x^{6}+1})
Solution:

Question 2.
(frac{1}{sqrt{1+4 x^{2}}})
Solution:

Question 3.
(frac{dx}{sqrt{(2-x)^{2}+1}})
Solution:

Question 4.
(frac{dx}{sqrt{9-25 x^{2}}})
Solution:

Question 5.
(frac{3 x}{1+2 x^{4}})
Solution:

Question 6.
(frac{x^{2}}{1-x^{6}})
Solution:

Question 7.
(frac{x-1}{sqrt{x^{2}-1}})
Solution:

Question 8.
(frac{x^{2}}{sqrt{x^{6}+a^{6}}})
Solution:

Question 9.
(frac{1}{sqrt{7-6 x-x^{2}}})
Solution:

Question 10.
(frac{1}{sqrt{x^{2}+2 x+2}})
Solution:

Question 11.
(frac{1}{9 x^{2}+6 x+5})
Solution:

Question 12.
(frac{1}{sqrt{7-6 x-x^{2}}})
Solution:

Question 13.
(frac{1}{sqrt{(x-1)(x-2)}})
Solution:

Question 14.
(frac{1}{sqrt{8+3 x-x^{2}}})
Solution:

Question 15.
(frac{1}{sqrt{(x-a)(x-b)}})
Solution:

Question 16.
(frac{4 x+1}{sqrt{2 x^{2}+x-3}})
Solution:

Question 17.
(frac{x+2}{sqrt{x^{2}-1}})
Solution:

Question 18.
(frac{5 x-2}{1+2 x+3 x^{2}})
Solution:

Question 19.
(frac{6 x+7}{sqrt{(x-5)(x-4)}})
Solution:

Question 20.
(frac{x+2}{sqrt{4 x-x^{2}}})
Solution:

Question 21.
(frac{x+2}{sqrt{x^{2}+2 x+3}})
Solution:

Question 22.
(frac{x+3}{x^{2}-2 x-5})
Solution:

Question 23.
(frac{5 x+3}{sqrt{x^{2}+4 x+10}})
Solution:

Choose the correct answers in the following questions 24 and 25:
Question 24.
∫(frac{d x}{x^{2}+2 x+2}) equals
(A) x tan^-1(x + 1) + C
(B) tan^-1(x + 1) + C
(C) (x + 1) tan^-1x + C
(D) tan^-1x + C
Solution:
∫(frac{d x}{x^{2}+2 x+2}) = ∫(frac{d x}{(x+1)^{2}+1}) = tan^-1 (x + 1) + C
∴ Part (B) is the correct answer.

Question 25.
Let I = ∫(frac{d x}{sqrt{9 x-4 x^{2}}}) equals
(A) (frac{1}{9}) sin^-1 ((frac{9x-8}{8})) + C
(B) (frac{1}{2}) sin^-1 ((frac{8x-9}{9})) + C
(C) (frac{1}{3}) sin^-1 ((frac{9x-8}{8})) + C
(D) (frac{1}{2}) sin^-1 ((frac{9x-8}{8})) + C
Solution:

∴ Part (B) is the correct answer.