Question

Integration of cotx(cosecx-1)e^x dx

plz help
am not able to solve it :'(

Answer 1

http://www.wolframalpha.com/input/?i=Integration+of+cotx%28cosec+x-1%29e%5Ex+dx

Answer 2

This should not be in the school :P

Answer 3

it is :P cbse question

Answer 4

If WolframAlpha says that it uses new functions, it is not in school syllabus :P

Answer 5

@kc_kennylau -even my teacher was not able to solve it it's just one mark question but still no one is able to get the answr if that was not a cbse sample paper question then 100 % it was incorrect question

Answer 6

lol it is

Answer 7

again this question has been posted in yahoo answer so i was thinking this time may be i will get the answer but still i m not able to solve it lol there must be something in thsi question that's y people are not able to sovle it

Answer 8

yes, it was incorrect question, it uses newly defined functions

Answer 9

yeah correct version shoudl be like tjhis
e^x(cotx-cosec^2x)dx

Answer 10

So, do you recognize any kind of relationship between cot(x) and -csc^2(x)?

Answer 11

Similarly, d/dx(tanx)=sec^2(x). This is fairly similar, but with cotangent and cosecant.

Answer 12

Using the correct versions its a simple integration by parts problem I believe.

Answer 13

@malevolence19 it's much easier than that. It's a simple substitution problem.

Answer 14

But you have:
\[\int e^x (\cot x-\csc^2 x)dx\]
With the e^x you still have integration by parts yes?

Answer 15

Finding the integrals of cotangent and cosecant squared are easy enough but I'm not seeing what substitution would help honestly, maybe I'm tired. :/

Answer 16

So if you you pick:\[u=e^x \cot x\]\[du=(e^x \cot x - e^x \csc^2x) dx\]