Integration (Indefinite)

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

Click on each question to see answer & solution.

Question No: #51

`\int \ \frac{dx}{1 + \tan x}`
Ans: `x/2 + 1/2 log |sinx + cosx| + c`
SEE SOLUTION

Question No: #52

`\int \ \frac{dx}{1 + \cot x}`
Ans: `x/2 - 1/2 log |sinx + cosx| + c`
SEE SOLUTION

Question No: #53

`\int \ \frac{dx}{a + b \tan x}`
Ans: `\frac{1}{a^2+b^2} [ax + b log |a cosx + b sinx | ] + c`
SEE SOLUTION

Question No: #54

`\int \ \frac{dx}{1 + \text{cosec} \ x}`
Ans: `secx - tanx + x +c`
SEE SOLUTION

Question No: #55

`\int \ \sqrt{1 + \sin \frac{x}{2}} \ dx`
Ans: `4(\sin\frac{x}{4} - \cos\frac{x}{4}) + c`
SEE SOLUTION

Question No: #56

`\int \ \sqrt{1 + \text{cosec} \ x} \ dx`
Ans: `sin^{-1}(2\sinx-1)+c`
SEE SOLUTION

Question No: #57

`\int \ \sqrt{1 + \sec x} \ dx`
Ans: `sin^{-1}(1-2\cosx)+c`
SEE SOLUTION

Question No: #58

`\int \ \frac{dx}{1 + \sin x - \cos x}`
Ans: `log|\frac{\tan\frac{x}{2}}{\tan\frac{x}{2}+1}|+c`
SEE SOLUTION

Question No: #59

`\int \ \frac{dx}{2 + \sin x + \cos x}`

Question No: #60

`\int \ \frac{dx}{3 + 2 \sin x + \cos x}`