how do you integrate sec^4(x) * tan(x)?

1 ⤊

how do you integrate sec^4(x) * tan(x)?

2007-07-12 16:19:27 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

4 answers

sec^4(x) * tan(x)
=1/(cos^4x) . sinx/cosx
= sin x / cos ^5 x

So make the substitution
u = cos x
du = -sinx dx

Int( - u^(-5) du)
= u^(-4) /4 +k
= (sec^4 x )/ 4 +k

2007-07-12 16:27:32 · answer #1 · answered by Anonymous · 0⤊ 0⤋

integ(sec^3 x )(sec x tan x) dx
= sec^4 x / 4 + c

2007-07-12 16:26:59 · answer #2 · answered by CPUcate 6 · 0⤊ 0⤋

Let u = sec(x)
then du = sec(x)tan(x)dx
∫u^3du = (1/4)u^4
∫sec^4(x) * tan(x)dx = (1/4)sec^4(x) + C

2007-07-12 16:28:19 · answer #3 · answered by Helmut 7 · 1⤊ 1⤋

sec^4(x)*tan(x)

=4sec(x)*tan(x)

=4[1/sin(x)]*[sin(x)/cos(x)]

=4csc(x)

just verify the range of the cosecant function

2007-07-12 16:29:32 · answer #4 · answered by nikkiwahine 2 · 0⤊ 2⤋