How do you find int cot^2x*tan^2xdxcot2xtan2xdx?

2 Answers
Apr 10, 2018

I=x+cI=x+c

Explanation:

We know that,

color(red)((1)tantheta*cottheta=1(1)tanθcotθ=1

Here,

I=intcot^2xtan^2xdxI=cot2xtan2xdx

I=int(cotxtanx)^2dx...toApply(1)

=int(1)^2dx

=x+c

Note:The question is more related to trigonometry than calculus ?!!!

x+c

rarrwhere c is the constant of integration.

Explanation:

Note that : cot^2x=1/tan^2x
rArr cot^2x.tan^2x =(1/cancel(tan^2x)).cancel(tan^2x)=1

Now we have only left 1.dx so our integral becomes :-

intcot^2x.tan^2xdx=int1dx

:.intcot^2x.tan^2xdx=x+c ; for some constant c