Home > Calculus > Integration by Trigonometric Substitution

How do you integrate #int sec^3xtanx#?

Answer 1

Christopher Allers

See below.

I would use a simple #u# substitution.

#intsec^3xtanxdx#

#u=secx#

#du=secxtanxdx#

#=>intu^2du#

#=>1/3u^3+C#

#=>(sec^3x)/3 +C#

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Answer 2

Evelyn Agard

#intsec^3(x)tan(x)dx=sec^3(x)/3+C#

Using integration by substitution:

Let #u = sec(x) => du = sec(x)tan(x)dx#

then

#intsec^3(x)tan(x)dx = intsec^2(x)(sec(x)tan(x))dx#

#=intu^2du#

#=u^3/3+C#

#=sec^3(x)/3+C#

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Answer 3

Axel Alvarez

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.