# GSEB Solutions Class 12 Maths Chapter 7 Integrals Ex 7.4

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.4 Textbook Questions and Answers.

## 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.
âˆ«$$\frac{d x}{x^{2}+2 x+2}$$ 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:
âˆ«$$\frac{d x}{x^{2}+2 x+2}$$ = âˆ«$$\frac{d x}{(x+1)^{2}+1}$$ = tan-1 (x + 1) + C
âˆ´ Part (B) is the correct answer.

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

âˆ´ Part (B) is the correct answer.