• Best of luck to the class of 2019 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • Like us on facebook here

help (1 Viewer)

tutor01

Member
Joined
Jul 21, 2005
Messages
44
Gender
Male
HSC
N/A
I am trying to find the integral of dx/(3+4sin(2x)). Can anyone help? Thanks!
 

tutor01

Member
Joined
Jul 21, 2005
Messages
44
Gender
Male
HSC
N/A
was hoping for a solution. t=tanx and from there. Is that best? Thanks.
 

pikachu975

I love trials
Moderator
Joined
May 31, 2015
Messages
2,398
Location
NSW
Gender
Male
HSC
2017
was hoping for a solution. t=tanx and from there. Is that best? Thanks.
I reckon splitting sin2x into 2sinxcosx could work too.

t = tan(x/2)
x = 2tan^-1 (t)
dx = 2dt/(1+t^2)

Integral of 1/(3+8(2t/1+t^2)(1-t^2 /1+t^2)) * 2dt/(1+t^2)

Go from there, just simplify then integrate
 

integral95

Well-Known Member
Joined
Dec 16, 2012
Messages
755
Gender
Male
HSC
2013
Yes I believe t = tan x would be a better substitution in this integral.
 

integral95

Well-Known Member
Joined
Dec 16, 2012
Messages
755
Gender
Male
HSC
2013
Wolfram alpha gives an inverse hyperbolic tan function. So have fun.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top