Question

Integrate. sec^3(x)

Answer 1

\[\sec^3 x \implies \sec^2 x \times \sec x\]
does that help?

Answer 2

Not really because there isn't much I could do. If I change that to (1+tan^2x) secx then there is nothing much I could do.

Answer 3

really? /:)

Answer 4

\[\int (\tan^2 x + 1)\sec x dx \implies \int \tan^2 x \sec x dx + \int \sec x dx\]

Answer 5

But I'll have and extra tan.

Answer 6

lol i stand corrected...that first term will be complicated...

Answer 7

seems integration by parts

Answer 8

a complicated one

Answer 9

well a long one

Answer 10

\[\int\limits \tan^{2}xsecx => \int\limits\frac{\sin^{2}x}{\cos^{2}x} *\frac{1}{cosx} => \int\limits\frac{1-\cos^{2}x}{\cos^{2}x} *\frac{1}{cosx} => \int\limits\frac{1}{\cos^{2}x} -\frac{\cos^{2}x}{\cos^{2}x} *\frac{1}{cosx} => \int\limits \sec^{2}x-1-secx \]

Answer 11

lol why didnt i think of that

Answer 12

\[\int\limits\frac{1}{\cos^{2}x} -\frac{\cos^{2}x}{\cos^{2}x} *\frac{1}{cosx} => \int\limits \sec^{2}x-1-secx \]

Answer 13

Might work..

Answer 14

I was thinking about that, I forgot about breaking it up.

Answer 15

Then you know what to do next?

Integrate one by one.

Answer 16

Yes, I know what to do.

Answer 17

\[\int\limits \sec^{2}xdx - \int\limits1 dx -\int\limits secx dx\]

Answer 18

for \(secx\) you can either integrate it by multiplying top and bottom by \(secx+tanx\)
Or use weierstrass substitution.