# How do you find the integral of #sec^5 x dx#?

##### 1 Answer

Write your answer here...

Start with a one sentence answer

Then teach the underlying concepts

Don't copy without citing sources

preview

?

#### Answer

Write a one sentence answer...

#### Answer:

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

Aug 29, 2017

#### Answer:

#### Explanation:

at first we will break

These show that

Then:

#intsec^3*sec^2xdx#

#=sec^3xtanx-inttanx*3sec^3xtanxdx#

Grouping

#=sec^3xtanx- int3sec^3x(sec^2x-1)dx#

#=sec^3xtanx-int(3sec^5x-3sec^3x)dx#

So

#intsec^5xdx=sec^3x*tanx-3intsec^5xdx+3intsec^3xdx#

#4intsec^5xdx=sec^3x*tanx+3intsec^3xdx#

And we know that

So

#4intsec^5xdx=sec^3x*tanx+3(1/2secxtanx+1/2lnabs(secx+tanx))#

#intsec^5xdx=1/4sec^3x*tanx+3/8secxtanx+3/8lnabs(secx+tanx)+C#

Was this helpful? Let the contributor know!

Describe your changes (optional) 200