Question

evalute the integral (sin^3 (x)/cosx)dx

Answer 1

hi @jasper21dude

write sin^3 x = sin^2 x (sin x dx)
and then plug in u= cos x

Answer 2

try that substitution and tell me what u get ?

Answer 3

you may write sin^3(x) /cos(x) as tan^3 (x) sec^2(x)
now a substitution of tanx = t should help .

Answer 4

I mean both methods are fine. Second one perhaps a bit shorter ?

Answer 5

difference of one or 2 steps is not actually a difference, both methods are equivalent :)

Answer 6

hmm..right.

Answer 7

tan^3 (x) sec^2(x) = sin^3(x)/cos^3(x) * 1/cos^2(x) = sin^3(x)/cos^5(x)
@shubhamsrg

Answer 8

it means not equal (sin^3 (x)/cosx)

Answer 9

oohhh....hemight have thought, tan^3 x cos^2 x ...which doesn't help i guess.....

Answer 10

my idea is
(sin^3 (x)/cosx)
= sin^2 (x) sinx/cosx)
= (cos^2 x - 1) sinx/cosx
= sinxcosx - tanx
= 1/2 sin2x - tanx

so, it becomes
int 1/2 sin2x dx - int tanx dx

Answer 11

damn... thts wrong too :)

Answer 12

yes, just that sin^2x = 1- cos^2 x

Answer 13

well, corrction :)
(sin^3 (x)/cosx)
= sin^2 (x) sinx/cosx)
= (1 - cos^2(x) ) sinx/cosx
= tanx - sinxcos
= tanx - 1/2sin2x

so, it is
int tan(x) dx - 1/2 int sin2x dx =

Answer 14

that should be easy for you
@jasper21dude

Answer 15

alternatively, after
= (1 - cos^2(x) ) sinx/cosx
if we put u= cos x
du = -sin x dx
we get, integral of (u^2-1)/u
which is equally easy to integrate (just don't forget to substitute back u=cos x)

Answer 16

wow, interesting :)

Answer 17

oops! :P
sorry..