Calculus 2: trying to intergrate 6sec^3 dx

[CajunHoss87]

Hi I'm trying to intergrate 6sec^3 dx and I'm having trouble.

I have 6integral (tanx^2+1)*secx dx but I am stuck.

What do I do?

 

[galactus]

Re: Calculus 2

$\displaystyle \int sec^{3}(x)dx$

We can just use the general reduction formula:

$\displaystyle \int sec^{n}(x)dx=\frac{sec^{n-2}(x)tan(x)}{n-1}+\frac{n-2}{n-1}\int sec^{n-2}(x)dx$

 

[Deleted member 4993]

Re: Calculus 2

Hi I'm trying to intergrate 6sec^3 dx and I'm having trouble.

I have 6integral (tanx^2+1)*secx dx but I am stuck.

What do I do?

$\displaystyle \int \sec^3(x) dx=\tan(x).sec(x) -\int tan^2(x).sec(x)dx=tan(x).sec(x) - \int[sec^2(x)-1].sec(x)dx$

$\displaystyle \int \sec^3(x) dx \, = \, \frac{1}{2}[tan(x).sec(x) + ln[|sec(x)+tan(x)|]]$