Question

The Integral of e^[sec(pi*t)]sec(pi*t)tan(pi*t)

Answer 1

\(\large \color{#000000}{\displaystyle\int\limits_{~}^{~} e^{\sec (\pi t)}\sec (\pi t)\tan (\pi t) ~dt}\)

Answer 2

\(\color{#000000 }{ \displaystyle \frac{ d }{dt}\sec(at)=a\sec(at)\tan(at) }\)

(using the chain rule) ... correct??

Answer 3

I worked through the problem, but the answer in the book is \[(1/\pi)e^(\sec \pi*t)\]

Answer 4

And I just got \[e^(\sec \pi*t)\]

Answer 5

How did you get that, can you show me your work?

Answer 6

Well the derivative of e^x is just e^x

Answer 7

and then I used the chain rule on sec(pi*t)

Answer 8

My problem is finding where the (1/pi) came from

Answer 9

What is the derivative of sec(π•t) ?

Answer 10

sec(pi*t)tan(pi*t)

Answer 11

tnope, you forgot the chain rule for π

Answer 12

for pi t

Answer 13

Oh I forgot. Thanks so much. Chain rule always gets me

Answer 14

:)

Answer 15

So, basically: (I'll use x)

\( \color{#000000 }{ \displaystyle \int e^{\sec \pi x} \sec(\pi x)\tan(\pi x)~dx }\)

\( \color{#000000 }{ \displaystyle \int \left(\frac{1}{\pi}\times \pi\right)e^{\sec \pi x} \sec(\pi x)\tan(\pi x)~dx }\)

\(\color{#000000 }{ \displaystyle \frac{1}{\pi}\int e^{\sec \pi x} [ \pi \sec(\pi x)\tan(\pi x)]~dx }\)

Answer 16

then either u-substitution u=sec(π•x),
or "recognize the derivative" which is just the same thing...