salparadise64
need help proving reduction formula for calc
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salparadise64
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please...
salparadise64
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@roadjester
roadjester
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who's the author of your book?
roadjester
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Stewart?
salparadise64
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james stewart
roadjester
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What edition?
salparadise64
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calculus early transcendental 7th E
salparadise64
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@abb0t
roadjester
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Damn, I've got Calculus 6th oh well
roadjester
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Let me think; haven't done calc in a while
salparadise64
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hmmmmm
roadjester
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I'm just gonna BS this, maybe something will come to me.
\(\int{tan^nxdx=\int tan^{n-1}}(x) tan(x)dx\)
salparadise64
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pg 469 section 7.1 #53
salparadise64
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yeah, i have the solution manual too, i was hoping someone would be able to explain it.
roadjester
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oookkaay; I think the solution is self-explanatory...
myininaya
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\[\int\limits_{}^{}\tan^n dx=\int\limits_{}^{}\tan^{n-2}(x)\tan^2(x) dx=\int\limits_{}^{}\tan^{n-2}(x)(\sec^2(x)-1) dx\]
\[=\int\limits_{}^{}\tan^{n-2}(x)\sec^2(x)-\int\limits_{}^{}\tan^{n-2}(x) dx\]
do a sub
let u=tan(x)
du=sec^2(x) dx
and you will see you are almost done
salparadise64
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@myininaya thank you!