Question

Indefinite integral of (tan^5 x)*(sec^4 x)dx

Can't seem to figure out which identities to substitute in...

Answer 1

\[\int\limits_{?}^{?}tanx^{5 }*secx^4\]
something like this i suppose?

Answer 2

undo a chain rule .....

Answer 3

\[\int\limits_{}^{}\tan^{5} (x)\sec^{4}(x)dx\]

Answer 4

take tanx^2 +1 =secx^2

Answer 5

oooooh

Answer 6

it becomes tanx^5 * (tanx^2+1)secx^2
(tanx^7+tanx^5)secx^2
you get two integrals
tanx^7 * secx^2 + tanx^5 * secx^2

Answer 7

And then substitue u=tan(x), du=sec^2(x), right? and it all simplifies to
[tan^6(x)]/6 + [tan^8(x)]/8 + C. Thanks.