Integration (Indefinite)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #71

`\int \ \frac{d\theta}{\sin (\theta - \frac{\pi}{2}) \sin (\theta - \frac{\pi}{4})}`

Question No: #72

`\int \ \frac{x^2 + \sin^2 x}{1 + x^2} \ \sec^2 x \ dx`

Question No: #73

`\int \ \frac{x^2 + \sin^2 x}{1 + x^2} \ dx`

Question No: #74

`\int \ \frac{\cos \theta}{(1 - \sin \theta)(2 - \sin \theta)} \ d\theta`

Question No: #75

`\int \ \frac{\cos \theta}{(1 + \sin \theta)(2 + \sin \theta)} \ d\theta`

Question No: #76

`\int \ \frac{1 + \tan^2 x}{1 + \cot^2 x} \ dx`

Question No: #77

`\int \ \frac{\tan x}{a + b \tan^2 x} \ dx`

Question No: #78

`\int \ \frac{\tan x}{\sqrt{a + b \tan^2 x}} \ dx \ \ \ (b \gt a)`
Ans: `-\frac{1}{\sqrt{b-a}} \sin^{-1}{\frac{(\sqrt{b} - \sqrt{a}) \cos x}{\sqrt{b}}} + c`
SEE SOLUTION

Question No: #79

`\int \ \frac{\tan x \sec^2x}{a^2 + b^2 \tan^2 x} \ dx`

Question No: #80

`\int \ \frac{dx}{\sec^2 x + \tan^2 x} \ dx`