Question

evaluate the following : evaluate the following : @Mathematics

Answer 1

\[\int\limits_{}^{}e ^{x}\cos x(1-\cot x).dx\]

Answer 2

try trigonometric substitution!

Answer 3

how???

Answer 4

http://www.wolframalpha.com/input/?i=integrate+%28e%5E%28x%29+*+cos%28x%29+*+%281%E2%88%92cot%28x%29%29%29

Answer 5

how did they proceeded
i need the steps
plssssssssssssss

Answer 6

I have no idea how they proceeded. I'm only at the level of calculus 2!

Answer 7

wait a minute
e^x( cosx - cosx*cotx) Hmm...

e^x*cosx - e^x*cos^2x/sin x



hey just try by parts, just do it I am sure things will get simple

Answer 8

cot x's derivative is coesc^2x, right?

Answer 9

yep

Answer 10

@ishaan: i tried it out but it didn't work!!!

Answer 11

Now integrate the two function separately. To integrate e^x cos x, integrate by parts twice. I.e., let \( J =\int e^x \cos x dx \).

Then
\[ J = e^x \sin x - \int e^x \sin x \ dx \]
\[ = e^x \sin x - \left( - e^x \cos x + \int e^x \cos x \ dx \right) \]
\[ = e^x (\sin x + \cos x) - J\]
and therefore
\[ J = \frac{1}{2} e^x (\sin x + \cos x) \]

Answer 12

what about e^x*cosx*cotx?

Answer 13

@James: what about the other part of the question???

Answer 14

are you sure it's cot x, not tan x?

Answer 15

ya it is!!!

Answer 16

Yeah wish it was tan x

Answer 17

because it's very ugly and there's no elegant solution; or rather, no expression in terms of elementary functions, as the Wolfram solution demonstrates.

Answer 18

k!!!!

Answer 19

thanks guyz

Answer 20

DASHINI chck your question again

Answer 21

i am damn sure about the question

Answer 22

it ok i'll better ask my teacher if possible

Answer 23

The other integral you posted all is tough, it requires quite alot of work.

Answer 24

they won't give you the question, if it's beyond you

Answer 25

thats better tanks

Answer 26

there must be a way, keep looking for it...
I will see if I can get through this