Mathematics

Evaluate: $$\displaystyle\int {\dfrac{1+\cos 4x}{\cot x-\tan x}dx}$$


SOLUTION
$$\int { \cfrac { 1+\cos { 4x }  }{ \cot { x } -\tan { x }  }  } dx=\int { \cfrac { 1+2\cos ^{ 2 }{ 2x } -1 }{ \cfrac { \cos { x }  }{ \sin { x }  } -\cfrac { \sin { x }  }{ \cos { x }  }  }  } dx$$
$$=\int { \cfrac { 2\cos ^{ 2 }{ 2x } .\sin { x } \cos { x }  }{ \cos ^{ 2 }{ x }- \sin ^{ 2 }{ x }  }  } dx=\int { \cfrac { \cos ^{ 2 }{ 2x } .\sin { 2x }  }{ \cos { 2x }  }  } dx$$
$$=\int { \cos { 2x } .\sin { 2x }  } dx=\cfrac { 1 }{ 2 } \int { 2\sin { 2x } .\cos { 2x }  } dx$$
$$=\cfrac { 1 }{ 2 } \int { \sin { 4x }  } dx=-\cfrac { 1 }{ 8 } \cos { 4x } +C$$
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium

$$\displaystyle \int_{1}^{\infty}\left( \frac { 1 }{ 1+x^{ 2 } }  \right) d{ x }=$$

  • A. $$-\displaystyle \frac{\pi}{4}$$
  • B. $$\displaystyle \frac{\pi}{2}$$
  • C. $$-\displaystyle \frac{\pi}{2}$$
  • D. $$\displaystyle \frac{\pi}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Evaluate $$\displaystyle\int^{\pi/6}_0\sec^2xdx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard
The value of $$\displaystyle \lim_{n\to\infty}  \displaystyle \sum_{r=1}^{n}\frac{1}{n}\sqrt{\frac{n+r}{n-r}}$$ is
  • A. $$\displaystyle \frac{\pi}{2}$$
  • B. $$ 2\pi$$
  • C. $$\displaystyle \frac{\pi}{2}-1$$
  • D. $$\displaystyle \frac{\pi}{2}+1$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Solve 
$$\int (sinx + cos x )^2. dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Single Correct Medium
If $$\dfrac{3x^{2}+10x+13}{(x-1)^{4}}=\dfrac{A}{(x-1)^{2}}+\dfrac{B}{(x-1)^{3}}+\dfrac{C}{(x-1)^{4}}$$ then descending order of $$A,B,C$$
  • A. $$A, B, C$$
  • B. $$A, C, B$$
  • C. $$C, A, B$$
  • D. $$C, B, A$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer