Integration (Indefinite)

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

Click on each question to see answer & solution.

Question No: #31

`\int \ \frac{dx}{\sin^2 x \cos x} \ dx`
Ans: `log|secx + tanx| - cscx + c`
SEE SOLUTION

Question No: #32

`\int \ \frac{\sec x}{\sec x + \tan x} \ dx`
Ans: `tanx - secx + c`
SEE SOLUTION

Question No: #33

`\int \ \frac{\sin^8 x - \cos^8 x}{1 - 2 \sin^2 x \cos^2 x} \ dx`
Ans: `-\frac{sin2x}{2} + c`
SEE SOLUTION

Question No: #34

`\int \ \frac{\sin^6x - \cos^6x}{1 - 2 \sin^2x \cos^2x} \ dx`
Ans: `- \frac{1}{4\sqrt{2}}\ log| \frac{\sqrt{2}+sin2x}{\sqrt{2} - sin2x} | - 1/4 sin2x + c`
SEE SOLUTION

Question No: #35

`\int \ \frac{\sin^6x + \cos^6x}{\sin^2x \cos^2x} \ dx`
Ans: `tanx - cotx - 3x + c`
SEE SOLUTION

Question No: #36

`\int \ \frac{\sin^6x - \cos^6x}{\sin^2x \cos^2x} \ dx`
Ans: `2 csc2x + 1/2 sin2x + c`
SEE SOLUTION

Question No: #37

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

Question No: #38

`\int \ \frac{\cos 2x}{\sin^4x + \cos^4x} \ dx`
Ans: `\frac{1}{2\sqrt{2}} log|\frac{\sqrt{2}+sin2x}{\sqrt{2}-sin2x}| + c`
SEE SOLUTION

Question No: #39

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

Question No: #40

`\int \ \frac{\sin 4x}{\sqrt{1 + \cos 4x}} \ dx`