Ask your own question, for FREE!
Mathematics 41 Online
OpenStudy (anonymous):

This is the question of integration by parts and it is killing me Integration of e^(m* inverse of sinx) dx

OpenStudy (anonymous):

\[\int\limits e ^{m \sin^{-1} x} dx\]

OpenStudy (anonymous):

use \[\sin^{-1}x=t \]

OpenStudy (anonymous):

Integration of parts is so fun though =/ remember the acronym LIPET for what to use as your "u" in your integration by parts Logs Inverses Polynomials Exponential Trig In this case, separate it first into e^m * e^inverse sinx only thing that trips me up here is that you integrating with respect to x but where does m come from....I'd just assume it to be a constant and therefore you can do the backwards power rule to antiderive it.

OpenStudy (anonymous):

=> x=sint => dx=cost dt so the expressio becomes \[\int\limits e^{mt}costdt\] now use integration by parts

OpenStudy (anonymous):

I tried everything but the solution which I am getting is not matching the solution given in the textbook

OpenStudy (anonymous):

@ vamgadu I tried but the answer is no matching the texttbook answer

OpenStudy (dumbcow):

i agree with vamgadu ^ do you get this answer http://www.wolframalpha.com/input/?i=integrate+e^%28mt%29+cos%28t%29+dt then you have to plug sin(x) in for t

OpenStudy (anonymous):

\[ dv = dx \\ u= e^{m \sin ^{-1}(x)}\\ v= x\\ du=\frac{m e^{m \sin ^{-1}(x)}}{\sqrt{1-x^2}}\\ u v - \int v du =x e^{m \sin ^{-1}(x)}-\frac{m \left(m x-\sqrt{1-x^2}\right) e^{m \sin ^{-1}(x)}}{m^2+1}=\\ \frac{\left(m \sqrt{1-x^2}+x\right) e^{m \sin ^{-1}(x)}}{m^2+1} \]

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
MakaylaChuck23: Help wats this
2 hours ago 1 Reply 0 Medals
MakaylaChuck23: uh oh
2 hours ago 1 Reply 0 Medals
Treeko: Pics I took w my friend !
4 hours ago 6 Replies 1 Medal
Aliciaa: Is anyone elses QC going wack? Mine keeps freezing and stuff
2 hours ago 26 Replies 0 Medals
autumnp: does anyone have bandlab?
4 hours ago 4 Replies 0 Medals
Jeromeccv: Art for @vanessad123
2 hours ago 49 Replies 4 Medals
ohhhhhhhhhhhhhh: how do i slim my waist fast
4 hours ago 4 Replies 1 Medal
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!