Integration (Indefinite)

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

Click on each question to see answer & solution.

Question No: #21

`\int \ \frac{\cos 5x + \cos 4x}{1-2 \cos 3x} \ dx`
Ans: `-( \frac{\sin 2x}{2} + \sin x ) + c`
SEE SOLUTION

Question No: #22

`\int \ \frac{\cos 7x + \cos 5x}{1 - 2 \cos 4x} \ dx`
Ans: `-sinx - \frac{sin3x}{3} + c`
SEE SOLUTION

Question No: #23

`\int \ \frac{\cos 8x - \cos 7x}{1 + 2 \cos 5x} \ dx`
Ans: `\frac{sin 2x}{2} - \frac{sin 3x}{3} + c`
SEE SOLUTION

Question No: #24

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

Question No: #25

`\int \ \sec^2 x \cos^2 2x \ dx`
Ans: `\tan x + \sin 2x - 2x + c`
SEE SOLUTION

Question No: #26

`\int \ \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} dx`
Ans: `2 (sinx + x\cos\alpha) + c`
SEE SOLUTION

Question No: #27

`\int \ \sin^4 x \ dx`
Ans: `1/8 (3x + \frac{sin4x}{4} - 2sin2x) + c`
SEE SOLUTION

Question No: #28

`\int \ \cos^4 x \ dx`
Ans: `1/8 (3x + \frac{sin4x}{4} + 2sin2x) + c`
SEE SOLUTION

Question No: #29

`\int \ \tan^2 x \ dx`
Ans: `tanx - x + c`
SEE SOLUTION

Question No: #30

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