Question

evaluate integration e^x(x+1)/sin^2(xe^x)​

Answer 1

Answer:

-Cot(xe^x)

Step-by-step explanation:

This question was asked in my recent 12th board exam recently... It was asked in a 1 mark MCQ type question

You proceed by taking x(e^x) as t and therefore dt=e^x(x+1)DX

So the integral reduces to

dt/(sint)^2 which you can write as (cosect)^2dt which is a standard integral which is equal to -cot(t)

Therefore answer is -Cot(xe^x)