Question

This is not a riddle! well kinda riddlish >:))

how to integrate \(\LARGE \int{}{} \frac{1}{\cos x} dx\) step-by-step

Answer 1

I was gonna say Weierstrass substitution but meh, too long.

Answer 2

idk :'( I can use integration by parts but @Mimi_x3 has a better way to do it.

Answer 3

@Mimi_x3 is a calculus expert huh

Answer 4

Turn 1/cos(x) to sec(x) and multiply both numerator and denominator by sec(x)+tan(x).

Answer 5

Yeah, that's what Mimi does. The blockcoder way.

Answer 6

then \(\LARGE \frac{\sec^{2} x + secxtanx}{secxtanx}\)

Answer 7

what does that mean o.O

Answer 8

let u = secx tanx ??

Answer 9

There's a missing + in the denominator. =))

Answer 10

\[\int secx \frac {secx+tanx}{secx+tanx} dx\]\[=\int \frac {sec^x+secxtanx}{secx+tanx} dx\]\[=\int \frac {1}{secx+tanx} d(secx+tanx)\] =ln |secx + tanx| +C

Answer 11

where'd that second to the last line come from again?

Answer 12

\[\frac{d}{dx} (secx + tanx) = sec^2x + secxtanx\]

Answer 13

oh i see

Answer 14

so it was let u = secx + tanx right...

Answer 15

Perhaps... It should be... I don't know... I just did it in this way. Sorry!!!

Answer 16

i like u substitution :P hmm..so this doesnt have the trig substitution yet...gotta find one