Integration problem?

Question

i was given task of integrating sin(t) / 5 + ln(t)

I separated into integral of sin(t) * 5 + ln(t)

not sure where to go after this. All I need is a step in the right direction. Thank you!

Answer 1

How did you mean that you separated it but changing the / to a *  or maybe I'm missing something.  I came up with (-tcos(t))/(5+ln(t))

But my teacher taught his own way of intergration so I don't know if it would be much help.  But if you use the standard intergration method just use (5+ln(t)) for u and that would give you du=1/t

I dont think you would use integration by parts because there is not a function within a function.  Simple substitution should work.  Also I wasn't completely sure if the 5+ln(t) was all in the denominator.

Answer 2

use integration by parts formula. Let sin(t) = u and 5+ln(t) = v' then plug into the formula... google it if you have to

Answer 3

integrate[(1/5)*sin(t)+ ln(t)]

=

-cos(t)/5+ t*ln(t)-t+c

integrate(1/5 sin(t))=-cos(t)/5

use Integration by parts for ln(t):

let:

u = ln(t)

du = (1/t) dt    "d(u)/dt=1/t"

  

dv = dt

v = t   "from integrate(dv)=integrate(dt) above"

integration by parts formula:

= uv - v du

into this formula substitute:

u=ln(t), v=t, and du=(1/t)dt

= ln(t) (t) - (t) (1/t) dt

= ln(t) t - integrate[ t (1/t) dt]

= ln(t) t - integrate[ dt]

= t ln(t) - t + C.