∫ sec 3x tan 3x dx?

0 ⤊

∫ sec 3x tan 3x dx?

Identify "u"
integration formula

2007-07-11 16:13:00 · 3 answers · asked by Cantthinkofanickname 1 in Science & Mathematics ➔ Mathematics

3 answers

u = 3x
du = 3 dx
dx = du / 3

∫ sec 3x tan 3x dx
=
1/3 ∫ sec u tan u du
= 1/3 (sec u) + C
= 1/3 (sec 3x) + C

2007-07-11 16:17:19 · answer #1 · answered by whitesox09 7 · 0⤊ 0⤋

Let u = 3x
du = 3 dx
dx = du / 3
I = (1/3) â« sec u tan u du
I = (1/3) sec u + C
I = (1/3) sec 3x + C

2007-07-12 04:00:48 · answer #2 · answered by Como 7 · 0⤊ 0⤋

Note that

sec 3x tan 3x = d/dx (sec 3x)

So you can eliminate the derivate with the integral to have just

sec 3x + C

Summarizing:

â« sec 3x tan 3x dx = sec 3x + C

2007-07-11 23:37:16 · answer #3 · answered by Gearld GTX 4 · 0⤊ 1⤋