logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
0 votes

Integrate: $\int -cosec ^2 (\log x ) + \cot (\log x) dx$

$(a)\;\cot x + cosec x +c \\(b)\;x.\cot (\log x)+c \\(c)\;x \cot x +c \\ (d)\;None$

Can you answer this question?
 
 

1 Answer

0 votes
$\log x =t $
differentiate both sides
$dx=e^t.dt$
$\int e^t(cosec^2 t +\cot t)dt$
=> $\int (-) e^t cosec^2 t +\int e^t \cot t dt$
=> $\int (-) e^t cosec^2 t +e^t. \cot t -\int e^t cosec^2t dt$
=> $-\int e^t cosec^2 t +e^t. \cot t +\int e^t cosec^2t dt$
=> $ e^t \cot t+c$
=>$x.\cot (\log x)+c$
Hence b is the correct answer.
answered Dec 31, 2013 by meena.p
 
Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...