Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Stuck here, help me understand: - Integral Calculus - JEE Main-5

The value of \int \frac{x\, cotx\, cosecx}{\left ( x+cotx \right )^{2}}dx \: \: is equal to

  • Option 1)

    \frac{-1}{\left ( xtanx+1 \right )}+C

  • Option 2)

    \frac{-1}{\left ( xsinx+cosx \right )}+C

  • Option 3)

    \frac{-1}{\left ( x+cotx \right )}+C

  • Option 4)

    \frac{1}{\left ( xsinx+cosx \right )}+C

 

Answers (1)

best_answer

As we learnt

Type of integration by substitution -

\int \frac{f{}'(x)}{f(x)}dx=ln(f(x))+c

- wherein

Let f(x)=t  such that f{}'(x)dx=dt

 

 Let I=\int \frac{x\cot xcosecx}{\left ( x+\cot x \right )^{2}}dx=\int \frac{x\cot xcosecx}{\cot ^{2}x\left ( x\tan x+1 \right )^{2}}dx= \int \frac{x\cos x}{\left ( x\sin x+\cos x \right )^{2}}dx

=\frac{-1}{\left ( x\sin x+\cos x \right )}+C


Option 1)

\frac{-1}{\left ( xtanx+1 \right )}+C

Option 2)

\frac{-1}{\left ( xsinx+cosx \right )}+C

Option 3)

\frac{-1}{\left ( x+cotx \right )}+C

Option 4)

\frac{1}{\left ( xsinx+cosx \right )}+C

Posted by

gaurav

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: JCECEB invites fresh applications for Jharkhand state merit list correction

Latest Question