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

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

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

Evaluate the following Integrals.
Question 1.
(i) ∫\(\frac{\sqrt{2 x+3}}{x}\) dx
Solution:

(ii) ∫\(\frac{\sqrt{x^2-7}}{x}\) dx
Solution:

(iii) ∫\(\frac{\sqrt{x}}{x+2}\) dx
Solution:

(iv) ∫x\((3 x+2)^{\frac{1}{3}}\) dx
Solution:

(v) ∫\(\frac{x+2}{(2 x-1)^{\frac{1}{3}}}\) dx
Solution:

(vi) ∫(x + 2)\((x+1)^{\frac{1}{4}}\) dx
Solution:

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

(viii) ∫\(\frac{d x}{\sqrt{x}-\sqrt[3]{x}}\) (x = t⁶)
Solution:

Question 2.
(i) ∫\(\frac{3 x+4}{\sqrt{2 x-3}}\) dx
Solution:

(ii) ∫(7x + 4)\(\sqrt{3 x+2}\) dx
Solution:

(iii) ∫(3x + 1)\((x-2)^{\frac{9}{2}}\) dx
Solution:

(iv) ∫\(\frac{2 x+5}{(x+2)^{\frac{7}{2}}}\) dx
Solution:

(v) ∫\(\frac{x^2+2 x+1}{\sqrt{x+4}}\) dx
Solution:

(vi) ∫(x² + 2x + 7)\(\sqrt{x+1}\) dx
Solution:

Question 3.
(i) ∫\(\frac{d x}{\sqrt{4 x^2-4 x+5}}\)
Solution:

(ii) ∫\(\sqrt{4 x^2-4 x+5}\) dx
Solution:

(iii) ∫\(\frac{d x}{\sqrt{x^2-6 x+5}}\) dx
Solution:

(iv) ∫\(\sqrt{x^2-6 x+5}\) dx
Solution:

(v) ∫\(\frac{d x}{\sqrt{1+2 x-x^2}}\) dx
Solution:

(vi) ∫\(\sqrt{1+2 x-x^2}\) dx
Solution:

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

(ii) ∫\(\frac{d x}{(2-x) \sqrt{5-4 x+x^2}}\)
Solution:

Question 5.
(i) ∫\(\frac{d x}{(2 x+5) \sqrt{x+2}}\)
Solution:

(ii) ∫\(\frac{1+x^2}{x \sqrt{x^4+1}}\) dx
Solution:

(iii) ∫\(\sqrt{\frac{x-1}{2 x+1}}\) dx
Solution:

(iv) ∫\(\frac{x}{\left(a^2-x^2\right)\left(x^2-b^2\right)}\) dx
Solution: