Mathematics

$$\int { \cfrac { \csc ^{ 2 }{ x } -2005 }{ \cos ^{ 2005 }{ x }  } dx } $$ is equal to


ANSWER

$$\cfrac { \cot { x } }{ { \left( \cos { x } \right) }^{ 2005 } } +C$$


SOLUTION
$$\displaystyle\int \dfrac{\text{cosec}^{2}x-2005}{\cos^{2005}x}dx$$
Put $$t=\dfrac{\cot x}{\cos ^{2005}x}\implies dt=\dfrac{\text{cosec}^{2}x(\cos^{2005}x)-(\cot x)(2005\cos^{2004}x\sin x)}{(\cos^{2005}x)^{2}}dx$$ 
                                               $$=\dfrac{\text{cosec}^{2}x-2005}{\cos^{2005}x}dx$$
$$\displaystyle\int dt=t+C=\dfrac{\cot x}{\cos^{2005}x}+C$$

View Full Answer

Its FREE, you're just one step away


Single Correct 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
$$\displaystyle \int x \tan^{-l} (x^{2})dx=$$
  • A. $$\displaystyle \frac{1}{2}[x^{2}\tan^{-1}(x^{2})+\log(1+x^{4})]+c$$
  • B. $$x^{2}\tan^{-1}(x^{2})-\displaystyle \frac{1}{2}\log(1+x^{4})+c$$
  • C. $$x^{2}\tan^{-1}(x^{2})+\displaystyle \frac{1}{2}\log(1+x^{4})+c$$
  • D. $$\displaystyle \frac{1}{2}[x^{2}\tan^{-1}(x^{2})-\frac{1}{2}\log(1+x^{4})]+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Hard
$$I = \displaystyle \int \sec x\tan x dx$$ is
equal to
  • A. $$\cos x+c$$
  • B. $$\tan x+c$$
  • C. None of these
  • D. $$\sec x+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
$$\displaystyle\int \dfrac{dx}{\sqrt{10-10x-2x^2}}$$=?

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
$$\displaystyle \int\frac{dx}{x(1+\sqrt[3]{x})^{2}}$$ is equal to
  • A. $$3(\displaystyle \log\frac{1+\sqrt[3]{x}}{\sqrt[3]{x}}+\frac{1}{1+\sqrt[3]{x}})+c$$
  • B. $$3(\displaystyle \log\frac{x^{1/3}}{1+x^{1/3}}-\frac{1}{1+\sqrt[3]{x}})+c$$
  • C. $$3(\displaystyle \log\frac{1+\sqrt[3]{x}}{\sqrt[3]{x}}-\frac{1}{1+\sqrt[3]{x}})+c$$
  • D. $$3(\displaystyle \log\frac{x^{1/3}}{1+x^{1/3}}+\frac{1}{1+\sqrt[3]{x}})+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
Evaluate:
$$ \int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer