Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

See more answers at brainly.com

\[\int\limits \tan^3 x secx dx\]

what to do?

\[ \tan^3 x \sec x = \tan x \sec x ( \sec^2 x - 1)\]
seems like it will get the same

yeah ..next step

note that d(sec x) =sec x tan x dx

yes all right

what's next..

let u = sec x then proceed.
du= sec x tan x dx
so it all becomes \(\int (u^2 - 1) du\)

dear are you solving integral by parts?

or by substituion?

it will become like this i guess u^3/3 - u +c

yes next step..

eh? \(\int u^n du= \frac{u^{n+1}}{n+1} +C\)

after applying we ll get as i above wrote ?

you'll get the answer....from integrating the above eq.

wait let me write what i am getting.

\[\frac{ \sec^3x }{ 3 }- secx +c = answer ???\]

it should be, yeah. :) you can always check your answers with wolfram.

wolfram.?

http://www.wolframalpha.com/input/?i=integrate%20tan%5E3%20x%20sec%20x%20dx&t=crmtb01

but answer is differnet in my book?

\[\frac{ 1 }{ 3 }(secxtan^2x-2secx)+c =answer ( book)\]

just take sec x out. and also, the integral, \(\int du=u\)

did't get..

i have already written this.Scroll up a bit

i just wanna get the same answer as in my book...:)

i have three books with same answer(:

lol i dun think wolfram's wrong, in anycase....lol

if we solve this by ''integration by parts'' rather tha by substituion?

\[\int\limits uvdx= u \int\limits vdx - \int\limits(\int\limits vdx) u'dx\]

thanks i took your time