Integration (Indefinite)

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

Click on each question to see answer & solution.

Question No: #41

`\int \ \frac{\sin x}{\sqrt{1 + \sin x}} \ dx`
Ans: `2(sin\frac{x}{2}-cos\frac{x}{2}) - 1/\sqrt{2} log |tan(x/2+\pi/8)| + c`
SEE SOLUTION

Question No: #42

`\int \ \frac{\sin x}{\sqrt{1 - \sin x}} \ dx`

Question No: #43

`\int \ \frac{1 + \cos x}{1 - \cos x} \ dx`

Question No: #44

`\int \ \frac{1 - \sin x}{1 + \sin x} \ dx`
Ans: `2tanx - x - 2secx+ c`
SEE SOLUTION

Question No: #45

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

Question No: #46

`\int \ \frac{dx}{1 - \sin x}`

Question No: #47

`\int \ \frac{dx}{4 + \sin x}`
Ans: `2/\sqrt{15} tan^{-1}{4/\sqrt{15} (tan \frac{x}{2} + 1/4)} + c`
SEE SOLUTION

Question No: #48

`\int \ \frac{dx}{1 + \cos 2x}`

Question No: #49

`\int \ \frac{dx}{1 + \cos 2x}`
Ans: `1/2 tanx + c`
SEE SOLUTION

Question No: #50

`\int \ \frac{dx}{2 + \cos x}`
Ans: `2/\sqrt{3} tan^{-1}(1/\sqrt{3} tan\frac{x}{2})+c`
SEE SOLUTION