need help proving reduction formula for calc

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need help proving reduction formula for calc

Mathematics
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please...
who's the author of your book?

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Other answers:

Stewart?
james stewart
What edition?
calculus early transcendental 7th E
Damn, I've got Calculus 6th oh well
Let me think; haven't done calc in a while
hmmmmm
I'm just gonna BS this, maybe something will come to me. \(\int{tan^nxdx=\int tan^{n-1}}(x) tan(x)dx\)
pg 469 section 7.1 #53
yeah, i have the solution manual too, i was hoping someone would be able to explain it.
oookkaay; I think the solution is self-explanatory...
\[\int\limits_{}^{}\tan^n dx=\int\limits_{}^{}\tan^{n-2}(x)\tan^2(x) dx=\int\limits_{}^{}\tan^{n-2}(x)(\sec^2(x)-1) dx\] \[=\int\limits_{}^{}\tan^{n-2}(x)\sec^2(x)-\int\limits_{}^{}\tan^{n-2}(x) dx\] do a sub let u=tan(x) du=sec^2(x) dx and you will see you are almost done
@myininaya thank you!

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