Math question

[Scrapster]

Find the integral of:

/
/
/
| sin(x)tan(x)dx
\
\
/
/

I left my calc book at home and don't have any identities with me.

any suggestions?

 

[iamwiz82]

integral of sin(x)tan(x)dx is:


-cos(x)(sec^2)(x) + C, i believe, correct me if i am wrong here. it can probably be reduced though.

 

[Scrapster]

back that azz up

 

[d0ofy]

I get:

cos(x)ln|cos(x)|+C

 

[slipperyslope]

get a TI89. It will do it for you

Jim

 

[iamwiz82]

d0ofy is right, i forgot the tan law.

 

[d0ofy]

The calculator is great if you're looking for numerical values, but he's looking for it in terms trig functions. Unless I'm mistaken. I have a TI-89 and I still had to remember the identities.

 

[d0ofy]

iamwiz82:
You must have gotten mixed up because the intergral of sec^2(x)=tan(x).

 

[ArkAoss]

oh boy, calculus, you have it memorized?

 

[Demon-Xanth]

42

 

[thEnEuRoMancER]

d0ofy, how did you get your solution? Differentiating your solution doesn't yield sinxtanx...

sinxtanx=sin^2x/cosx=(1-cos^2x)/cosx=1/cosx-cosx

integral(1/cosx-cosx)dx=integral(1/cosx)dx-integral(cosx)dx=ln|tg(x/2+pi/4)|-sinx+C

 

[hendon]

sin(x)tan(x)
= sin^2(x)/cos(x)
= [ 1 - cos^2(x) ]/ cos(x)
= sec(x) - cos(x)

Therefore,
Integral of (sin(x)tan(x))
= Integral of (sec(x) - cos(x))
= ln|sec(x)+tan(x)| - sin(x)

 

[d0ofy]

I used the identities.
Integral of sin(x)= -cos(x)
Integral of tan(x)= -ln |cos(x)|

Maybe I used them incorrectly?

 

[Napalm381]

Yes doofy, you used them incorrectly. The integral of a product is not the product of the integrals.

 

[d0ofy]

Duh me. Perhaps that explains my C in Calc3.