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 (e^4x = 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) ∫$\frac{d x}{\sqrt{e^{4 x}-5}}$ (e^2x = 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: