Question

The integral of ((4sin*squared*x cos*squared*x divided by sin2xcos2x))dx help :3

Answer 1

know ur trig

Answer 2

simplify the integrand first, this is more of a trig problem... not calculus :)

Answer 3

i wouldn't post this if im good at my trig :D

Answer 4

il give a hint maybe :

\(\large 2\sin (x) \cos( x) = \sin(2x)\)

Answer 5

does that help ? :)

Answer 6

im trying :)

Answer 7

okie, take ur time :)

Answer 8

\(\large \int \frac{4\sin^2x \cos^2x}{\sin(2x) \cos(2x)} ~dx\)

Answer 9

the integrand is like that right ?

Answer 10

yup

Answer 11

okay, take the numerator :

\(\large 4\sin^2x \cos^2x\)

\(\large (2\sin x \cos x)^2\)

appeal to the earlier identity(hint) :
\(\large \left(\sin (2x)\right)^2\)

Answer 12

see if that looks okay...

Answer 13

then, the integrand becomes :


\(\large \frac{\left(\sin(2x)\right)^2}{\sin(2x) \cos(2x)} \)

Answer 14

so the answer will be -1/2 ln *absolute value of* cos2x + C???

Answer 15

Looks you nailed it !!

Answer 16

Yup, thats the correct answer :)

Answer 17

thank you :D

Answer 18

np... u wlc :)