IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

a4asd

what is the intigral of

cos²x/(1+tan²x)

i will rate you five times

aditya_arora04

Well,

Here is the solution :

when you arithematically solve it you get cos⁴x.

Now,

cos⁴x

=> (1+cos2x)²/ 4

=> (1 + cos²2x + 2cos2x)

=> [1 + cos2x + (1+cos4x)/2 ] /4

now, you can well integrate cos2x and cos4x easily !!!!!

you will get your answer !!!!!!!

And yes, no need to rate five times, once would do !!!!!!!

thevyzz

easy

put sec^2 x = 1+ tan^2 x

so, it becomes

integral cos^4 x

now integrate

dinesh_ddt

spideyunlimited

cos⁴x

=

cos²x(1 - sin²x)

put 1 - sin²x = t

bumba

cos⁴x dx

=

(1+cos 2x)^2/4 dx

=1/4

1+2 cos 2x +cos ^2x dx

=1/4[

1 dx +2

cos 2x + 1/2

1 +cos 4x]

then we can integrate these simple terms and obtain the required result.

a4asd

hey this is
cos^2x/(1+tanx)