Question

need help proving reduction formula for calc

Answer 1

please...

Answer 2

@roadjester

Answer 3

who's the author of your book?

Answer 4

Stewart?

Answer 5

james stewart

Answer 6

What edition?

Answer 7

calculus early transcendental 7th E

Answer 8

@abb0t

Answer 9

Damn, I've got Calculus 6th oh well

Answer 10

Let me think; haven't done calc in a while

Answer 11

hmmmmm

Answer 12

I'm just gonna BS this, maybe something will come to me.
\(\int{tan^nxdx=\int tan^{n-1}}(x) tan(x)dx\)

Answer 13

pg 469 section 7.1 #53

Answer 14

yeah, i have the solution manual too, i was hoping someone would be able to explain it.

Answer 15

oookkaay; I think the solution is self-explanatory...

Answer 16

\[\int\limits_{}^{}\tan^n dx=\int\limits_{}^{}\tan^{n-2}(x)\tan^2(x) dx=\int\limits_{}^{}\tan^{n-2}(x)(\sec^2(x)-1) dx\]
\[=\int\limits_{}^{}\tan^{n-2}(x)\sec^2(x)-\int\limits_{}^{}\tan^{n-2}(x) dx\]
do a sub
let u=tan(x)
du=sec^2(x) dx
and you will see you are almost done

Answer 17

@myininaya thank you!