# CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Ex 9(d)

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 9 Integration Ex 9(d) Textbook Exercise questions and Answers.

## CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Exercise 9(d)

Question 1.
(i) ∫$$\frac{d x}{\sqrt{11-4 x^2}}$$
Solution:

(ii) ∫$$\frac{e^{3 x}}{\sqrt{4-e^{6 x}}}$$dx
Solution:

(iii) ∫$$\frac{d x}{\sqrt{25-(\ln x)^2}}$$
Solution:

(iv) ∫$$\frac{\cos \theta}{\sqrt{4-\sin ^2 \theta}}$$dθ
Solution:

(v) ∫$$\frac{x^2}{\sqrt{36-x^6}}$$dx (x3 = z)
Solution:

(vi) ∫$$\frac{x+3}{\sqrt{9-x^2}}$$dx
Solution:

(vii) ∫$$\frac{d x}{\sqrt{5-x^2-4 x}}$$ (x + 2 = z)
Solution:

(viii) ∫$$\frac{x+3}{\sqrt{5-x^2-4 x}}$$dx
Solution:

Question 2.
(i) ∫$$\frac{d x}{3 x^2+7}$$
Solution:

(ii) ∫$$\frac{e^{4 x}}{e^{8 x}+4}$$dx (e4x = z)
Solution:

(iii) ∫$$\frac{d x}{x\left\{(\ln x)^2+25\right\}}$$
Solution:

(iv) ∫$$\frac{\sec \theta \tan \theta}{\sec ^2 \theta+4}$$dθ
Solution:

(v) ∫$$\frac{x^9}{x^{20}+4}$$dx (x10 = z)
Solution:

(vi) ∫$$\frac{3 x+4}{x^2+4}$$dx
Solution:

(vii) ∫$$\frac{d x}{x^2+6 x+13}$$ (x + 3 = z)
Solution:

(viii) ∫$$\frac{x+5}{x^2+6 x+13}$$dx
Solution:

Question 3.
(i) ∫$$\frac{d x}{x \sqrt{4 x^2-9}}$$
Solution:

(ii) ∫$$\frac{d x}{\sqrt{e^{4 x}-5}}$$ (e2x = z)
Solution:

(iii) ∫$$\frac{d x}{x \ln x \sqrt{(\ln x)^2-4}}$$
Solution:

(iv) ∫$$\frac{\sec \theta d \theta}{\sin \theta \sqrt{3 \tan ^2 \theta-1}}$$
Solution:

(v) ∫$$\frac{d x}{x \sqrt{x^{14}-b^2}}$$ (x7 = z)
Solution:

(vi) ∫$$\frac{x^2+3}{x \sqrt{x^2-4}}$$dx
Solution:

(vii) ∫$$\frac{d x}{(x+1) \sqrt{x^2+2 x-3}}$$ (x + 1 = z)
Solution:

(viii) ∫$$\frac{x^2+2 x+4}{(x+1) \sqrt{x^2+2 x-3}}$$ dx
Solution:

Question 4.
(i) ∫$$\frac{d x}{\sqrt{3 x^2+4}}$$
Solution:

(ii) ∫$$\frac{4 e^x}{\sqrt{3 e^x+4}}$$dx
Solution:

(iii) ∫$$\frac{d x}{x \sqrt{(\ln x)^2+8}}$$
Solution:

(iv) ∫$$\frac{d \theta}{\sin ^2 \theta \sqrt{\cot ^2 \theta+2}}$$
Solution:

(v) ∫$$\frac{x^2}{\sqrt{x^6+a^6}}$$dx
Solution:

(vi) ∫$$\frac{3 x+4}{\sqrt{5 x^2+8}}$$dx
Solution:

(vii) ∫$$\frac{e^x \cos e^x}{\sqrt{\sin ^2 e^x+9}}$$dx
Solution:

(viii) ∫$$\frac{2 x+11}{\sqrt{x^2+10 x+29}}$$dx (x + 5 = z)
Solution:

Question 5.
(i) ∫$$\frac{d x}{\sqrt{4 x^2-6}}$$
Solution:

(ii) ∫$$\frac{e^{5 x}}{\sqrt{e^{10 x}-4}}$$dx
Solution:

(iii) ∫$$\frac{d x}{x \sqrt{(\ln x)^2-4}}$$; x > e2
Solution:

(iv) ∫$$\frac{\cos \theta d \theta}{\sin ^2 \theta \sqrt{{cosec}^2 \theta-4}}$$
Solution:

(v) ∫$$\frac{d x}{\sqrt{x} \sqrt{x-a^2}}$$
Solution:

(vi) ∫$$\frac{x-2}{\sqrt{3 x^2-8}}$$dx
Solution:

(vii) ∫$$\frac{3 x+4}{x \sqrt{2 x^2-5}}$$dx
Solution:

(viii) ∫$$\frac{x^2+2 x+2}{x \sqrt{x^2-4}}$$dx
Solution:

(ix) ∫$$\frac{d x}{\sqrt{x^2+8 x}}$$
Solution:

(x) ∫$$\frac{x+7}{\sqrt{x^2+8 x}}$$dx
Solution: